{"id":3237,"date":"2020-11-16T09:25:49","date_gmt":"2020-11-16T08:25:49","guid":{"rendered":"http:\/\/jhmaths.fr\/?page_id=3237"},"modified":"2020-11-17T08:22:37","modified_gmt":"2020-11-17T07:22:37","slug":"fonction-inverse","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/terminale-technologique\/fonction-inverse\/","title":{"rendered":"Fonction inverse"},"content":{"rendered":"<p>[vc_row][vc_column][vc_column_text css_animation=\u00a0\u00bbnone\u00a0\u00bb el_class=\u00a0\u00bbchose\u00a0\u00bb el_id=\u00a0\u00bbobjectif-1&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Comportement de la fonction inverse<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]<b>La fonction inverse \\(x \\mapsto \\displaystyle \\frac{1}{x}\\) est d\u00e9finie pour tout r\u00e9el \\(x\\) diff\u00e9rent de 0 (c&rsquo;est-\u00e0-dire sur \\(-\\infty ; 0[ \\cup ]0 ; +\\infty[\\) , qui s&rsquo;\u00e9crit aussi \\(\\mathbb{R}^*\\) )<\/b>[\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]<b>La fonction inverse est d\u00e9croissante ;<\/b><\/p>\n<p>Plus \\(x\\) se rapproche de 0, plus son inverse \\(\\displaystyle \\frac{1}{x}\\) prend de grandes valeurs (elles tendent vers \\(-\\infty\\) si \\(x\\) est n\u00e9gatif et vers \\(+\\infty\\) si \\(x\\) est positif)<\/p>\n<p>&nbsp;<\/p>\n<p>Au contraire, plus \\(x\\) s&rsquo;\u00e9loigne de 0, plus son inverse \\(\\displaystyle \\frac{1}{x}\\) tend vers 0.[\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]<b>La fonction inverse est n\u00e9gative lorsque \\(x\\) est n\u00e9gatif, et positive lorsque \\(x\\) est positif.<\/b>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<div style=\"text-align: center;\">\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/Vl2rlbFF22Y\" width=\"320\" height=\"180\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]<\/p>\n<h2>Quizz<\/h2>\n<p><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-80\" class=\"h5p-iframe\" data-content-id=\"80\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"T Techno- Fonction inverse - propri\u00e9t\u00e9s de la fonction\"><\/iframe><\/div>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text css_animation=\u00a0\u00bbnone\u00a0\u00bb el_class=\u00a0\u00bbchose\u00a0\u00bb el_id=\u00a0\u00bbobjectif-2&Prime;]<\/p>\n<h1 style=\"text-align: center;\">Courbe et asymptotes<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]La courbe de la fonction inverse \\(x \\mapsto \\displaystyle \\frac{1}{x}\\) s&rsquo;appelle une hyperbole.<\/p>\n<p>Elle poss\u00e8de deux asymptotes qui sont les axes du rep\u00e8re (rappel dans la vid\u00e9o qui suit, attention elle est en anglais !).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-3241 aligncenter\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/11\/courbe-fct-inverse-300x300.jpg\" alt=\"\" width=\"300\" height=\"300\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/11\/courbe-fct-inverse-300x300.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/11\/courbe-fct-inverse-150x150.jpg 150w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/11\/courbe-fct-inverse-468x468.jpg 468w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/11\/courbe-fct-inverse-558x557.jpg 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/11\/courbe-fct-inverse-550x550.jpg 550w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/11\/courbe-fct-inverse-220x220.jpg 220w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/11\/courbe-fct-inverse.jpg 644w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<div style=\"text-align: center;\">\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/oBmnt5tXRws\" width=\"320\" height=\"180\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text css_animation=\u00a0\u00bbnone\u00a0\u00bb el_class=\u00a0\u00bbchose\u00a0\u00bb el_id=\u00a0\u00bbcomplements\u00a0\u00bb]<\/p>\n<h1 style=\"text-align: center;\">Un exemple d&rsquo;\u00e9quation<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]R\u00e9solution de l&rsquo;\u00e9quation \\(\\displaystyle \\frac{5-x}{x}-8 &gt; 11\\)[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<div style=\"text-align: center;\">\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/V07NxCl7Eto\" width=\"320\" height=\"180\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text css_animation=\u00a0\u00bbnone\u00a0\u00bb el_class=\u00a0\u00bbchose\u00a0\u00bb]<\/p>\n<h1 style=\"text-align: center;\">Un exemple d&rsquo;in\u00e9quation (rappel de seconde)<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]R\u00e9solution de l&rsquo;in\u00e9quation \\(\\displaystyle \\frac{2-6x}{3x-2}\\leq 0\\)[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text]<\/p>\n<div style=\"text-align: center;\">\n<p><iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/Vitm29q8AEs\" width=\"320\" height=\"180\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text css_animation=\u00a0\u00bbnone\u00a0\u00bb el_class=\u00a0\u00bbchose\u00a0\u00bb el_id=\u00a0\u00bbobjectif-3&Prime;]<\/p>\n<h1 style=\"text-align: center;\">D\u00e9riv\u00e9e de la fonction inverse<\/h1>\n<p>[\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]La d\u00e9riv\u00e9e de la fonction \\(x \\mapsto \\displaystyle \\frac{1}{x}\\) est la fonction \\(x \\mapsto \\displaystyle -\\frac{1}{x^2}\\).<\/p>\n<p>&nbsp;<\/p>\n<p>Cette d\u00e9riv\u00e9e est naturellement toujours n\u00e9gative puisque la fonction inverse est d\u00e9croissante.[\/vc_column_text][\/vc_column][vc_column width=\u00a0\u00bb1\/2&Prime;][\/vc_column][\/vc_row][vc_row][vc_column][vc_column_text]<\/p>\n<h2>Plan de travail<\/h2>\n<p>[\/vc_column_text][vc_single_image source=\u00a0\u00bbexternal_link\u00a0\u00bb onclick=\u00a0\u00bbimg_link_large\u00a0\u00bb img_link_target=\u00a0\u00bb_blank\u00a0\u00bb custom_src=\u00a0\u00bbhttps:\/\/docs.google.com\/drawings\/d\/e\/2PACX-1vSM0kkOfUopo1zVFTe-68R_r8rPo-u0373eZraCZ96663gAEYJze3B08FgRn-HXEmK0u1kIH0rfIGWF\/pub?w=960&amp;h=720&Prime;][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text css_animation=\u00a0\u00bbnone\u00a0\u00bb el_class=\u00a0\u00bbchose\u00a0\u00bb el_id=\u00a0\u00bbobjectif-1&Prime;] Comportement de la fonction inverse [\/vc_column_text][\/vc_column][\/vc_row][vc_row content_placement=\u00a0\u00bbmiddle\u00a0\u00bb][vc_column width=\u00a0\u00bb1\/2&Prime;][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]La fonction inverse \\(x \\mapsto \\displaystyle \\frac{1}{x}\\) est d\u00e9finie pour tout r\u00e9el \\(x\\) diff\u00e9rent de 0 (c&rsquo;est-\u00e0-dire sur \\(-\\infty ; 0[ \\cup ]0 ; +\\infty[\\) , qui s&rsquo;\u00e9crit aussi \\(\\mathbb{R}^*\\) )[\/vc_column_text][vc_column_text el_class=\u00a0\u00bbproprietepremieresthr propriete\u00a0\u00bb]La fonction inverse est d\u00e9croissante ; Plus \\(x\\) se rapproche [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3063,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-3237","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3237","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=3237"}],"version-history":[{"count":9,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3237\/revisions"}],"predecessor-version":[{"id":3248,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3237\/revisions\/3248"}],"up":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3063"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=3237"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=3237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}