### Home > CALC > Chapter 4 > Lesson 4.4.3 > Problem 4-151

4-151.

Define possible functions

*f*(*x*) and*g*(*x*) so that*h*(*x*) =*f*(*g*(*x*)). Remember*f*(*x*) ≠*x*, and*g*(*x*) ≠*x*. Homework Help ✎*h*(*x*) = (3*x*cos(*x*^{2}))^{3}*h*(*x*) = 1*h*(*x*) =*x*

*f*(*x*) =_____________*g*(*x*) = cos*x*

One possible solution:*f*(*x*) = *x*^{0}*g*(*x*) = *x*^{2}

Find another.

One possible solution:*f*(*x*) = *x*³*g*(*x*) = 3*x*cos(*x*²)

Find another.

Recall the definition of inverse functions:*f*(*x*) and *g*(*x*) are inverse functions if *f*(*g*(*x*)) = *x*