### Home > CALC > Chapter 4 > Lesson 4.4.3 > Problem4-151

4-151.

Define possible functions $f(x)$ and $g(x)$ so that $h(x) = f(g(x))$. Remember $f(x) ≠ x$, and $g(x) ≠ x$.

1. $h ( x ) = \sqrt [ 5 ] { \operatorname { cos } x }$

$f(x) =$_____________
$g(x) =\operatorname{cos}x$

1. $h(x) = (3x\operatorname{cos}(x^2))^3$

One possible solution:
$f(x) = x^³$
$g(x) = 3x\operatorname{cos}(x^²)$
Find another.

1. $h(x) = 1$

One possible solution:
$f(x) = x^0$
$g(x) = x^2$
Find another.

1. $h(x) = x$

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