### Home > APCALC > Chapter 4 > Lesson 4.4.3 > Problem4-161

4-161.

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

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

$f\left(x\right) = \text{_____________}$
$g\left(x\right)=\cos x$

2. $h(x)=(3x\cos(x^2))^3$

One possible solution:
$f\left(x\right)=x^3$
$g\left(x\right)=3x\cos\left(x^2\right)$
Find another.

3. $h(x) = 1$

One possible solution:
$f\left(x\right) = x^{0}$
$g\left(x\right) = x^{2}$
Find another.

4. $h(x) = x$

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