<\/p>\n
Consider the two functions: f(x) = 1-x and g(x) = 1\/x. We can compose them in two ways: f(g(x)) and g(f(x)). We can go further and compose these two new functions with themselves, and also with the old ones, in a number of ways. Keeping composing these functions with the new ones as they are generated and figure out simplified formulae for them in terms of the variable x.\u00a0<\/p>\n
a) How many distinct functions are there, including f and g themselves?<\/p>\n
b) List them<\/p>\n
c) How is each one composed from f and g?<\/p>\n
d) How do you know that these are all there are?<\/p>\n
e) For what real numbers are all these functions simultaneously defined?<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
Consider the two functions: f(x) = 1-x and g(x) = 1\/x. We can compose them in two ways: f(g(x)) and g(f(x)). We can go further and compose these two new functions with themselves, and also with the old ones, in a number of ways. Keeping composing these functions with the new ones as they are […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_joinchat":[]},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/182470"}],"collection":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/comments?post=182470"}],"version-history":[{"count":0,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/182470\/revisions"}],"wp:attachment":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/media?parent=182470"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/categories?post=182470"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/tags?post=182470"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}