{"id":6661,"date":"2011-03-25T01:58:20","date_gmt":"2011-03-25T01:58:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6661"},"modified":"2022-01-13T00:46:37","modified_gmt":"2022-01-13T00:46:37","slug":"f-e-outra-funcao-racional","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6661","title":{"rendered":"f \u00e9 outra fun\u00e7\u00e3o racional"},"content":{"rendered":"<p><ul id='GTTabs_ul_6661' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6661' class='GTTabs_curr'><a  id=\"6661_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6661' ><a  id=\"6661_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_6661'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>f \u00e9 uma fun\u00e7\u00e3o racional definida em $\\mathbb{R}\\backslash \\left\\{ -1,1 \\right\\}$ por \\[f(x)=\\frac{1}{1-{{x}^{2}}}\\]<\/p>\n<p>Encontre os reais a e b tais que, para todo o $x\\ne 1\\wedge x\\ne -1$,\u00a0\\[f(x)=\\frac{a}{1-x}+\\frac{b}{1+x}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6661' onClick='GTTabs_show(1,6661)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6661'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>f \u00e9 uma fun\u00e7\u00e3o racional definida em $\\mathbb{R}\\backslash \\left\\{ -1,1 \\right\\}$ por \\[f(x)=\\frac{1}{1-{{x}^{2}}}\\]<\/p>\n<p>Encontre os reais a e b tais que, para todo o $x\\ne 1\\wedge x\\ne -1$,\u00a0\\[f(x)=\\frac{a}{1-x}+\\frac{b}{1+x}\\]<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>Ora, \\[\\begin{array}{*{35}{l}}<br \/>\nf(x) &amp; = &amp; \\frac{a}{1-x}+\\frac{b}{1+x}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{a(1+x)}{(1-x)(1+x)}+\\frac{b(1-x)}{(1-x)(1+x)}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{(a-b)x+(a+b)}{1-{{x}^{2}}}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Dado que \\[f(x)=\\frac{1}{1-{{x}^{2}}}\\] vem:<\/p>\n<p>\\[\\begin{array}{*{35}{l}}<br \/>\n\\left\\{ \\begin{array}{*{35}{l}}<br \/>\na-b=0\u00a0 \\\\<br \/>\na+b=1\u00a0 \\\\<br \/>\n\\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}}<br \/>\n2a=1\u00a0 \\\\<br \/>\na+b=1\u00a0 \\\\<br \/>\n\\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}}<br \/>\na=\\frac{1}{2}\u00a0 \\\\<br \/>\nb=\\frac{1}{2}\u00a0 \\\\<br \/>\n\\end{array} \\right.\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6661' onClick='GTTabs_show(0,6661)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado f \u00e9 uma fun\u00e7\u00e3o racional definida em $\\mathbb{R}\\backslash \\left\\{ -1,1 \\right\\}$ por \\[f(x)=\\frac{1}{1-{{x}^{2}}}\\] Encontre os reais a e b tais que, para todo o $x\\ne 1\\wedge x\\ne -1$,\u00a0\\[f(x)=\\frac{a}{1-x}+\\frac{b}{1+x}\\] Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19483,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,147],"tags":[148],"series":[],"class_list":["post-6661","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-operacoes-com-funcoes","tag-operacoes-com-funcoes-2"],"views":2370,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/Funcao_f-P200_Ex59.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6661","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=6661"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6661\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19483"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6661"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}