{"id":28197,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/the-functions-f-and-g-are-defined-for-all-xer-101-by-fx-x11-x-and-gx1x-show-that-f%e2%97%8bg-1-x-f%e2%97%8bgx-how-to-do-this"},"modified":"2017-08-12T07:11:27","modified_gmt":"2017-08-12T07:11:27","slug":"the-functions-f-and-g-are-defined-for-all-xer-101-by-fx-x11-x-and-gx1x-show-that-f%e2%97%8bg-1-x-f%e2%97%8bgx-how-to-do-this","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/the-functions-f-and-g-are-defined-for-all-xer-101-by-fx-x11-x-and-gx1x-show-that-f%e2%97%8bg-1-x-f%e2%97%8bgx-how-to-do-this\/","title":{"rendered":"The functions f and g are defined for all x\u20acR { -1,0,1} by f(x) = (x+1)\/(1-x) and g(x)=1\/x . Show that (f\u25cbg)^-1 (x)= (f\u25cbg)(x). How to do this ?"},"content":{"rendered":"<p>General approach is to transform both sides of the equality until they start appearing similar.<\/p>\n<p>Consider the right hand side, we have: <\/p>\n<p>##(f@g)(x) = f(g(x)) = (1\/x +1)\/(1-1\/x) = (x+1)\/(x-1)## <\/p>\n<p>(defined since ##x=1## is not in the defined interval) (1)<\/p>\n<p>Consider the left hand side, we let: ##(f@g)^-1(x) = y## where ##(f@g)(y) = x##<\/p>\n<p>(according to definition of inverse function) From that, we can have : ##(f@g)(y) = (y+1)\/(y-1) = x## ##xy &#8211; x = y + 1 ## ##y = (x+1)\/(x-1)##= ##(f@g) ^-1 (x) ## <\/p>\n<p>(defined since x = 1 is not included in the defined interval) (2) Thus, from (1) &amp; (2), Q.E.D<\/p>\n","protected":false},"excerpt":{"rendered":"<p>General approach is to transform both sides of the equality until they start appearing similar. Consider the right hand side, we have: ##(f@g)(x) = f(g(x)) = (1\/x +1)\/(1-1\/x) = (x+1)\/(x-1)## (defined since ##x=1## is not in the defined interval) (1) <a href=\"https:\/\/www.benedictsol.com\/blogs\/the-functions-f-and-g-are-defined-for-all-xer-101-by-fx-x11-x-and-gx1x-show-that-f%e2%97%8bg-1-x-f%e2%97%8bgx-how-to-do-this\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-28197","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/28197","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=28197"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/28197\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=28197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=28197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=28197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}