{"id":11833,"date":"2014-02-28T01:39:54","date_gmt":"2014-02-28T01:39:54","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11833"},"modified":"2022-01-13T01:12:14","modified_gmt":"2022-01-13T01:12:14","slug":"mostre-que-as-funcoes-sao-iguais","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11833","title":{"rendered":"Mostre que as fun\u00e7\u00f5es s\u00e3o iguais"},"content":{"rendered":"<p><ul id='GTTabs_ul_11833' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11833' class='GTTabs_curr'><a  id=\"11833_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11833' ><a  id=\"11833_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_11833'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Mostre que as fun\u00e7\u00f5es seguintes s\u00e3o iguais.<\/p>\n<p>\\[\\begin{array}{*{20}{c}}<br \/>\n{\\begin{array}{*{20}{c}}<br \/>\n{f:}&amp;{\\mathbb{R}\\backslash \\left\\{ { &#8211; 3,3} \\right\\} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to \\frac{{x &#8211; 3}}{{{x^2} &#8211; 9}}}<br \/>\n\\end{array}}&amp;{}&amp;{\\text{e}}&amp;{}&amp;{\\begin{array}{*{20}{c}}<br \/>\n{g:}&amp;{\\mathbb{R}\\backslash \\left\\{ { &#8211; 3,3} \\right\\} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to \\frac{1}{{x + 3}}}<br \/>\n\\end{array}}<br \/>\n\\end{array}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11833' onClick='GTTabs_show(1,11833)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11833'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Mostre que as fun\u00e7\u00f5es seguintes s\u00e3o iguais.<\/p>\n<p>\\[\\begin{array}{*{20}{c}}<br \/>\n{\\begin{array}{*{20}{c}}<br \/>\n{f:}&amp;{\\mathbb{R}\\backslash \\left\\{ { &#8211; 3,3} \\right\\} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to \\frac{{x &#8211; 3}}{{{x^2} &#8211; 9}}}<br \/>\n\\end{array}}&amp;{}&amp;{\\text{e}}&amp;{}&amp;{\\begin{array}{*{20}{c}}<br \/>\n{g:}&amp;{\\mathbb{R}\\backslash \\left\\{ { &#8211; 3,3} \\right\\} \\to \\mathbb{R}} \\\\<br \/>\n{}&amp;{x \\to \\frac{1}{{x + 3}}}<br \/>\n\\end{array}}<br \/>\n\\end{array}\\]<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>Como \\[{D_f} = \\mathbb{R}\\backslash \\left\\{ { &#8211; 3,3} \\right\\} = {D_g}\\] e \\[f\\left( x \\right) = \\frac{{x &#8211; 3}}{{{x^2} &#8211; 9}} = \\frac{{x &#8211; 3}}{{\\left( {x + 3} \\right)\\left( {x &#8211; 3} \\right)}} = \\frac{1}{{x + 3}} = g\\left( x \\right),\\,\\forall x \\in {D_f}\\] ent\u00e3o as fun\u00e7\u00f5es $f$ e $g$ s\u00e3o iguais.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11833' onClick='GTTabs_show(0,11833)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Mostre que as fun\u00e7\u00f5es seguintes s\u00e3o iguais. \\[\\begin{array}{*{20}{c}} {\\begin{array}{*{20}{c}} {f:}&amp;{\\mathbb{R}\\backslash \\left\\{ { &#8211; 3,3} \\right\\} \\to \\mathbb{R}} \\\\ {}&amp;{x \\to \\frac{{x &#8211; 3}}{{{x^2} &#8211; 9}}} \\end{array}}&amp;{}&amp;{\\text{e}}&amp;{}&amp;{\\begin{array}{*{20}{c}} {g:}&amp;{\\mathbb{R}\\backslash \\left\\{ { &#8211; 3,3}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14083,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,147],"tags":[422,367,148],"series":[],"class_list":["post-11833","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-operacoes-com-funcoes","tag-11-o-ano","tag-igualdade-de-funcoes","tag-operacoes-com-funcoes-2"],"views":1643,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11833","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=11833"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11833\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11833"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11833"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11833"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11833"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}