### Home > INT3 > Chapter 5 > Lesson 5.2.1 > Problem 5-62

5-62.

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*) =*x*^{2}– 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*(*x*^{2} − 1).