Question by seanb: Composite functions?
What is a composite function, (inside/outside), and rules for range and domain?
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 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.
For example, consider f(whatever)= 1/(whatever-1) and g(whatever)=whatever 3.
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.
What do you think? Answer below!