{"id":11802,"date":"2014-02-24T00:01:27","date_gmt":"2014-02-24T00:01:27","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11802"},"modified":"2022-01-13T00:55:20","modified_gmt":"2022-01-13T00:55:20","slug":"verifique-se-sao-iguais-as-funcoes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11802","title":{"rendered":"Verifique se s\u00e3o iguais as fun\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_11802' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11802' class='GTTabs_curr'><a  id=\"11802_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11802' ><a  id=\"11802_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_11802'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Verifique se s\u00e3o iguais os seguintes pares de fun\u00e7\u00f5es reais de vari\u00e1vel real:<\/p>\n<ol>\n<li>\\[\\begin{array}{*{20}{l}}<br \/>\n{f\\left( x \\right) = \\frac{{2 &#8211; x}}{{{x^2} &#8211; 4}}}&amp;{\\text{e}}&amp;{g\\left( x \\right) = \\frac{{ &#8211; 1}}{{x + 2}}}<br \/>\n\\end{array}\\]<\/li>\n<li>\\[\\begin{array}{*{20}{l}}<br \/>\n{f\\left( x \\right) = \\frac{x}{{x &#8211; 1}}}&amp;{\\text{e}}&amp;{g\\left( x \\right) = \\frac{{{x^2} &#8211; x}}{{{{\\left( {x &#8211; 1} \\right)}^2}}}}<br \/>\n\\end{array}\\]<\/li>\n<li>\\[\\begin{array}{*{20}{l}}<br \/>\n{f\\left( x \\right) = \\frac{{{x^4} &#8211; 25}}{{{x^2} + 5}}}&amp;{\\text{e}}&amp;{g\\left( x \\right) = {x^2} &#8211; 5}<br \/>\n\\end{array}\\]<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11802' onClick='GTTabs_show(1,11802)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11802'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>\n<blockquote>\n<p>\\[\\begin{array}{*{20}{l}} \u00a0 {f\\left( x \\right) = \\frac{{2 &#8211; x}}{{{x^2} &#8211; 4}}}&amp;{\\text{e}}&amp;{g\\left( x \\right) = \\frac{{ &#8211; 1}}{{x + 2}}} \\end{array}\\]<\/p>\n<\/blockquote>\n<p>\u00ad<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{{D_f} = \\left\\{ {x \\in \\mathbb{R}:{x^2} &#8211; 4 \\ne 0} \\right\\} = \\mathbb{R}\\backslash \\left\\{ { &#8211; 2,2} \\right\\}}&amp;{\\text{e}}&amp;{{D_g} = \\left\\{ {x \\in \\mathbb{R}:x + 2 \\ne 0} \\right\\} = \\mathbb{R}\\backslash \\left\\{ { &#8211; 2} \\right\\}}<br \/>\n\\end{array}\\]<br \/>\nAs fun\u00e7\u00f5es n\u00e3o s\u00e3o iguais, pois ${D_f} \\ne {D_g}$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>\n<blockquote><p>\\[\\begin{array}{*{20}{l}} \u00a0 {f\\left( x \\right) = \\frac{x}{{x &#8211; 1}}}&amp;{\\text{e}}&amp;{g\\left( x \\right) = \\frac{{{x^2} &#8211; x}}{{{{\\left( {x &#8211; 1} \\right)}^2}}}} \\end{array}\\]<\/p><\/blockquote>\n<p>\u00ad<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{{D_f} = \\left\\{ {x \\in \\mathbb{R}:x &#8211; 1 \\ne 0} \\right\\} = \\mathbb{R}\\backslash \\left\\{ 1 \\right\\}}&amp;{\\text{e}}&amp;{{D_g} = \\left\\{ {x \\in \\mathbb{R}:{{\\left( {x &#8211; 1} \\right)}^2} \\ne 0} \\right\\} = \\mathbb{R}\\backslash \\left\\{ 1 \\right\\}}<br \/>\n\\end{array}\\]<br \/>\n\\[g\\left( x \\right) = \\frac{{{x^2} &#8211; x}}{{{{\\left( {x &#8211; 1} \\right)}^2}}} = \\frac{{x\\left( {x &#8211; 1} \\right)}}{{{{\\left( {x &#8211; 1} \\right)}^2}}} = \\frac{x}{{x &#8211; 1}} = f\\left( x \\right),\\,\\forall x \\in {D_f}\\]<br \/>\nAs fun\u00e7\u00f5es s\u00e3o iguais, pois ${D_f} = {D_g}$ e $f\\left( x \\right) = g\\left( x \\right),\\,\\forall x \\in {D_f}$.<br \/>\n\u00ad<\/li>\n<li>\n<blockquote><p>\\[\\begin{array}{*{20}{l}} \u00a0 {f\\left( x \\right) = \\frac{{{x^4} &#8211; 25}}{{{x^2} + 5}}}&amp;{\\text{e}}&amp;{g\\left( x \\right) = {x^2} &#8211; 5} \\end{array}\\]<\/p><\/blockquote>\n<p>\u00ad<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{{D_f} = \\left\\{ {x \\in \\mathbb{R}:{x^2} + 5 \\ne 0} \\right\\} = \\mathbb{R}}&amp;{\\text{e}}&amp;{{D_g} = \\left\\{ {x \\in \\mathbb{R}:\\left( {{x^2} &#8211; 5} \\right) \\in \\mathbb{R}} \\right\\} = \\mathbb{R}}<br \/>\n\\end{array}\\]<br \/>\n\\[f\\left( x \\right) = \\frac{{{x^4} &#8211; 25}}{{{x^2} + 5}} = \\frac{{\\left( {{x^2} + 5} \\right)\\left( {{x^2} &#8211; 5} \\right)}}{{{x^2} + 5}} = {x^2} &#8211; 5 = g\\left( x \\right),\\,\\forall x \\in {D_f}\\]<br \/>\nAs fun\u00e7\u00f5es s\u00e3o iguais, pois ${D_f} = {D_g}$ e $f\\left( x \\right) = g\\left( x \\right),\\,\\forall x \\in {D_f}$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11802' onClick='GTTabs_show(0,11802)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Verifique se s\u00e3o iguais os seguintes pares de fun\u00e7\u00f5es reais de vari\u00e1vel real: \\[\\begin{array}{*{20}{l}} {f\\left( x \\right) = \\frac{{2 &#8211; x}}{{{x^2} &#8211; 4}}}&amp;{\\text{e}}&amp;{g\\left( x \\right) = \\frac{{ &#8211; 1}}{{x + 2}}}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14113,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,147],"tags":[422,128],"series":[],"class_list":["post-11802","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-funcoes-2"],"views":3234,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat55.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11802","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=11802"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11802\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14113"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11802"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11802"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11802"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11802"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}