{"id":6695,"date":"2011-04-05T01:24:27","date_gmt":"2011-04-05T00:24:27","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6695"},"modified":"2021-12-26T16:12:52","modified_gmt":"2021-12-26T16:12:52","slug":"considere-a-funcao-real-de-variavel-real","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6695","title":{"rendered":"Considere a fun\u00e7\u00e3o real de vari\u00e1vel real"},"content":{"rendered":"<p><ul id='GTTabs_ul_6695' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6695' class='GTTabs_curr'><a  id=\"6695_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6695' ><a  id=\"6695_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_6695'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considere a fun\u00e7\u00e3o real de vari\u00e1vel real assim definida: \\[f(x)=5x+3\\]<\/p>\n<p>Mostre que as fun\u00e7\u00f5es $f\\circ f$ e ${{f}^{2}}$ s\u00e3o distintas.<\/p>\n<p>(${{f}^{2}}$ designa a fun\u00e7\u00e3o $f\\times f$,produto de $f$ por si pr\u00f3pria.)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6695' onClick='GTTabs_show(1,6695)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6695'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Ora, ${{D}_{f\\circ f}}=\\left\\{ x\\in \\mathbb{R}:x\\in {{D}_{f}}\\wedge f(x)\\in {{D}_{f}} \\right\\}=\\left\\{ x\\in \\mathbb{R}:x\\in \\mathbb{R}\\wedge (5x+3)\\in \\mathbb{R} \\right\\}=\\mathbb{R}$.<\/p>\n<p>E, $(f\\circ f)(x)=f(f(x))=f(5x+3)=5(5x+3)+3=25x+18$.<\/p>\n<p>Logo, \\[\\begin{array}{*{35}{l}}<br \/>\nf\\circ f: &amp; \\mathbb{R}\\to \\mathbb{R}\u00a0 \\\\<br \/>\n{} &amp; x\\to 25x+18\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Ora, ${{f}^{2}}(x)=f(x)\\times f(x)={{(5x+3)}^{2}}=25{{x}^{2}}+30x+9$.<\/p>\n<p>Logo, \\[\\begin{array}{*{35}{l}}<br \/>\n{{f}^{2}}: &amp; \\mathbb{R}\\to \\mathbb{R}\u00a0 \\\\<br \/>\n{} &amp; x\\to 25{{x}^{2}}+30x+9\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>As fun\u00e7\u00f5es s\u00e3o distintas, pois uma \u00e9 afim e a outra \u00e9 polinomial de grau dois.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6695' onClick='GTTabs_show(0,6695)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considere a fun\u00e7\u00e3o real de vari\u00e1vel real assim definida: \\[f(x)=5x+3\\] Mostre que as fun\u00e7\u00f5es $f\\circ f$ e ${{f}^{2}}$ s\u00e3o distintas. (${{f}^{2}}$ designa a fun\u00e7\u00e3o $f\\times f$,produto de $f$ por si pr\u00f3pria.)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14109,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,153],"tags":[154],"series":[],"class_list":["post-6695","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcao-composta","tag-funcao-composta-2"],"views":2450,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat51.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6695","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=6695"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6695\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14109"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6695"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6695"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6695"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6695"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}