When you stack one function machine on top of another so that the output of the first machine becomes the input of the second machine, you create a new function, which is a composition of the two functions. If the first function is f(x) and the second is g(x), the composition of the functions can be written as the composite function g(f(x)). Homework Help ✎
The function machines f(x) = x2 – 1 and g(x) = 3(x + 2) are stacked as shown at right. If x is input at the top, what expression comes out of the bottom? That is, what is the composite function g(f(x))?
Write an expression for the composite function f(g(x)).
This is g(x2 − 1).