{"id":11852,"date":"2014-04-29T16:04:41","date_gmt":"2014-04-29T15:04:41","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11852"},"modified":"2022-01-14T18:20:49","modified_gmt":"2022-01-14T18:20:49","slug":"caracterize-a-funcao-inversa-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11852","title":{"rendered":"Caracterize a fun\u00e7\u00e3o inversa"},"content":{"rendered":"<p><ul id='GTTabs_ul_11852' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11852' class='GTTabs_curr'><a  id=\"11852_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11852' ><a  id=\"11852_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_11852'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Caracterize a fun\u00e7\u00e3o inversa de cada uma das seguintes fun\u00e7\u00f5es:<\/p>\n<p>\\[\\begin{array}{*{20}{c}}<br \/>\n{f\\left( x \\right) = 6x + 5}&amp;{}&amp;{}&amp;{g\\left( x \\right) =\u00a0 &#8211; \\frac{{12}}{{x + 3}}}<br \/>\n\\end{array}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11852' onClick='GTTabs_show(1,11852)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11852'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>\\[\\begin{array}{*{20}{c}}<br \/>\n{f\\left( x \\right) = 6x + 5}&amp;{}&amp;{}&amp;{g\\left( x \\right) =\u00a0 &#8211; \\frac{{12}}{{x + 3}}}<br \/>\n\\end{array}\\]<\/p>\n<p>Como ${D_f} = D{&#8216;_f} = \\mathbb{R}$ e $y = 6x + 5 \\Leftrightarrow x = \\frac{{y &#8211; 5}}{6}$, ent\u00e3o: \\[\\begin{array}{*{20}{l}}<br \/>\n{{f^{ &#8211; 1}}:}&amp;{\\mathbb{R} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to \\frac{x}{6} &#8211; \\frac{5}{6}}<br \/>\n\\end{array}\\]<\/p>\n<p>Como ${D_g} = \\mathbb{R}\\backslash \\left\\{ { &#8211; 3} \\right\\}$, $D{&#8216;_g} = \\mathbb{R}\\backslash \\left\\{ 0 \\right\\}$ e $y =\u00a0 &#8211; \\frac{{12}}{{x + 3}} \\Leftrightarrow x =\u00a0 &#8211; 3 &#8211; \\frac{{12}}{y}$, ent\u00e3o: \\[\\begin{array}{*{20}{l}}<br \/>\n{{g^{ &#8211; 1}}:}&amp;{\\mathbb{R}\\backslash \\left\\{ 0 \\right\\} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to\u00a0 &#8211; 3 &#8211; \\frac{{12}}{x}}<br \/>\n\\end{array}\\]<\/p>\n<\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":760,\r\n\"height\":565,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 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Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19170,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,155],"tags":[422,156],"series":[],"class_list":["post-11852","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcao-inversa","tag-11-o-ano","tag-funcao-inversa-2"],"views":2277,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat61.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11852","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=11852"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11852\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19170"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11852"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11852"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11852"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11852"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}