{"id":6701,"date":"2011-04-05T23:36:46","date_gmt":"2011-04-05T22:36:46","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6701"},"modified":"2022-01-23T14:56:46","modified_gmt":"2022-01-23T14:56:46","slug":"use-a-calculadora-grafica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6701","title":{"rendered":"Use a calculadora gr\u00e1fica"},"content":{"rendered":"<p><ul id='GTTabs_ul_6701' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6701' class='GTTabs_curr'><a  id=\"6701_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6701' ><a  id=\"6701_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6701'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<ol>\n<li>Use a calculadora gr\u00e1fica e conjeture quais das seguintes fun\u00e7\u00f5es polinomiais t\u00eam fun\u00e7\u00e3o inversa:<br \/>\n<table class=\"aligncenter\" style=\"width: 80%;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">${{f}_{1}}(x)={{x}^{3}}-9{{x}^{2}}+5x-5$<\/td>\n<td style=\"text-align: center;\">${{f}_{2}}(x)=2x+{{x}^{2}}$<\/td>\n<td style=\"text-align: center;\">${{f}_{3}}(x)={{x}^{3}}-2{{x}^{2}}+5x-5$<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">${{f}_{4}}(x)=2x-{{x}^{2}}$<\/td>\n<td style=\"text-align: center;\">${{f}_{5}}(x)=2x+{{x}^{3}}$<\/td>\n<td style=\"text-align: center;\">${{f}_{6}}(x)=2x-{{x}^{3}}$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Para as que admitiu serem fun\u00e7\u00f5es injetivas, calcule a imagem, pela inversa, de 10, com aproxima\u00e7\u00e3o \u00e0s cent\u00e9simas.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6701' onClick='GTTabs_show(1,6701)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6701'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Para cada uma das seis fun\u00e7\u00f5es consideradas, tem-se:<br \/>\n<table class=\"aligncenter\" style=\"width: 600px;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<caption>${{f}_{1}}(x)={{x}^{3}}-9{{x}^{2}}+5x-5$<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6702\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6702\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J1.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"J1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J1.png\" class=\"alignnone size-full wp-image-6702\" title=\"J1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J1.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J1.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J1-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6703\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6703\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G1.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G1.png\" class=\"alignnone size-full wp-image-6703\" title=\"G1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G1.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G1.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G1-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\">A fun\u00e7\u00e3o <strong>n\u00e3o admite inversa<\/strong>, pois \u00e9 uma fun\u00e7\u00e3o n\u00e3o injetiva.<br \/>\nNote que h\u00e1 objetos diferentes com igual imagem (H\u00e1 retas horizontais que intersectam o gr\u00e1fico da fun\u00e7\u00e3o em mais do que um ponto).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"aligncenter\" style=\"width: 600px;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<caption>${{f}_{2}}(x)=2x+{{x}^{2}}$<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6704\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6704\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J2.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"J2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J2.png\" class=\"alignnone size-full wp-image-6704\" title=\"J2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J2.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J2.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J2-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6705\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6705\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G2.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G2.png\" class=\"alignnone size-full wp-image-6705\" title=\"G2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G2.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G2.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G2-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\">A fun\u00e7\u00e3o <strong>n\u00e3o admite inversa<\/strong>, pois \u00e9 uma fun\u00e7\u00e3o n\u00e3o injetiva.<br \/>\nNote que h\u00e1 objetos diferentes com igual imagem (H\u00e1 retas horizontais que intersectam o gr\u00e1fico da fun\u00e7\u00e3o em mais do que um ponto).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"aligncenter\" style=\"width: 600px;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<caption>${{f}_{3}}(x)={{x}^{3}}-2{{x}^{2}}+5x-5$<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6706\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6706\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J3.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"J3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J3.png\" class=\"alignnone size-full wp-image-6706\" title=\"J3\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J3.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J3.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J3-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6707\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6707\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3.png\" class=\"alignnone size-full wp-image-6707\" title=\"G3\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6708\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6708\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3b.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G3b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3b.png\" class=\"alignnone size-full wp-image-6708\" title=\"G3b\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3b.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3b.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3b-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3c.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6709\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6709\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3c.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G3c\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3c.png\" class=\"alignnone size-full wp-image-6709\" title=\"G3c\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3c.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3c.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G3c-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\">${{f}_{3}}'(x)=3{{x}^{2}}-4x+5$<br \/>\nComo ${{f}_{3}}'(x)&gt;0,\\forall x\\in \\mathbb{R}$, a fun\u00e7\u00e3o \u00e9 estritamente crescente e, portanto, \u00e9 injetiva.<br \/>\nA fun\u00e7\u00e3o <strong>admite inversa<\/strong>, pois \u00e9 uma fun\u00e7\u00e3o injetiva.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"aligncenter\" style=\"width: 600px;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<caption>${{f}_{4}}(x)=2x-{{x}^{2}}$<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6711\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6711\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J4.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"J4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J4.png\" class=\"alignnone size-full wp-image-6711\" title=\"J4\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J4.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J4.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J4-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6710\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6710\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G4.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G4.png\" class=\"alignnone size-full wp-image-6710\" title=\"G4\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G4.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G4.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G4-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\">A fun\u00e7\u00e3o <strong>n\u00e3o admite inversa<\/strong>, pois \u00e9 uma fun\u00e7\u00e3o n\u00e3o injetiva.<br \/>\nNote que h\u00e1 objetos diferentes com igual imagem (H\u00e1 retas horizontais que intersectam o gr\u00e1fico da fun\u00e7\u00e3o em mais do que um ponto).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"aligncenter\" style=\"width: 600px;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<caption>${{f}_{5}}(x)=2x+{{x}^{3}}$<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J5.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6712\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6712\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J5.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"J5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J5.png\" class=\"alignnone size-full wp-image-6712\" title=\"J5\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J5.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J5.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J5-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6713\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6713\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5.png\" class=\"alignnone size-full wp-image-6713\" title=\"G5\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6714\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6714\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5b.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G5b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5b.png\" class=\"alignnone size-full wp-image-6714\" title=\"G5b\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5b.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5b.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5b-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5c.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6715\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6715\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5c.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G5c\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5c.png\" class=\"alignnone size-full wp-image-6715\" title=\"G5c\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5c.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5c.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G5c-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\">${{f}_{5}}'(x)=2+3{{x}^{2}}$<br \/>\nComo ${{f}_{5}}'(x)&gt;0,\\forall x\\in \\mathbb{R}$, a fun\u00e7\u00e3o \u00e9 estritamente crescente e, portanto, \u00e9 injetiva.<br \/>\nA fun\u00e7\u00e3o <strong>admite inversa<\/strong>, pois \u00e9 uma fun\u00e7\u00e3o injetiva.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"aligncenter\" style=\"width: 600px;\" border=\"2\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<caption>${{f}_{6}}(x)=2x-{{x}^{3}}$<\/caption>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6717\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6717\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J6.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"J6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J6.png\" class=\"alignnone size-full wp-image-6717\" title=\"J6\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J6.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J6.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/J6-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6716\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6716\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G6.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G6.png\" class=\"alignnone size-full wp-image-6716\" title=\"G6\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G6.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G6.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/G6-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" colspan=\"2\">A fun\u00e7\u00e3o <strong>n\u00e3o admite inversa<\/strong>, pois \u00e9 uma fun\u00e7\u00e3o n\u00e3o injetiva.<br \/>\nNote que h\u00e1 objetos diferentes com igual imagem (H\u00e1 retas horizontais que intersectam o gr\u00e1fico da fun\u00e7\u00e3o em mais do que um ponto).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Com a aproxima\u00e7\u00e3o pedida, obt\u00e9m-se: $f_{3}^{-1}(10)\\approx 2,45$ e $f_{5}^{-1}(10)\\approx 1,85$.<br \/>\n(Ver gr\u00e1ficos correspondentes, acima.)<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6701' onClick='GTTabs_show(0,6701)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Use a calculadora gr\u00e1fica e conjeture quais das seguintes fun\u00e7\u00f5es polinomiais t\u00eam fun\u00e7\u00e3o inversa: ${{f}_{1}}(x)={{x}^{3}}-9{{x}^{2}}+5x-5$ ${{f}_{2}}(x)=2x+{{x}^{2}}$ ${{f}_{3}}(x)={{x}^{3}}-2{{x}^{2}}+5x-5$ ${{f}_{4}}(x)=2x-{{x}^{2}}$ ${{f}_{5}}(x)=2x+{{x}^{3}}$ ${{f}_{6}}(x)=2x-{{x}^{3}}$ Para as que admitiu serem fun\u00e7\u00f5es injetivas, calcule a imagem, pela&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20907,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,155],"tags":[156],"series":[],"class_list":["post-6701","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcao-inversa","tag-funcao-inversa-2"],"views":2693,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/11V2Pag204-75-b_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6701","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6701"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6701\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20907"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6701"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6701"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6701"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}