Question by seanb: Composite functions?
\nWhat is a composite function, (inside\/outside), and rules for range and domain?<\/p>\n
Best answer:
\nAnswer by Benjamin NIf a function is like a machine, then a composite function is like a composite machine: the output of the first one becomes the input of the second.<\/p>\n
f(g(x)) means “take x, run it through the g function, take the result, and run it through the f function”. There is a complication if the output (range) of g extends over values which are not allowed inputs (domain) for f. In this case you have to restrict the input values of x so that the output of the first stage fits into the second.<\/p>\n
For example, consider f(whatever)= 1\/(whatever-1) and g(whatever)=whatever 3.<\/p>\n
Then f(g(x))=f(x 3)=1\/(x 3-1)=1\/(x 2). Now this has a big problem when x=-2, so we have to disallow x=-2 as an input to the machine because even though g(2) is defined, f(g(2)) is not.<\/p>\n
What do you think? Answer below!<\/p>\n","protected":false},"excerpt":{"rendered":"
Question by seanb: Composite functions? What is a composite function, (inside\/outside), and rules for range and domain? Best answer: Answer by Benjamin NIf a function is like a machine, then a composite function is like a composite machine: the output of the first one becomes the input of the second. f(g(x)) means “take x, run […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[215,216],"class_list":["post-197","post","type-post","status-publish","format-standard","hentry","category-machining","tag-composite","tag-functions"],"yoast_head":"\n