### Home > APCALC > Chapter 3 > Lesson 3.3.2 > Problem3-104

3-104.

Define $f$ and $g$ such that $h(x) = f(g(x))$ for the following functions where $f(x)\ne x$ and $g(x)\ne x$.

1. $h(x) = (2x − 5)^3$

$g(x) = 2x − 5$
$f(x) = x^3$

1. $h(x)=\sin(3x−1)$

$g(x)$ is the inner function.
$f(x)$ is the outer function.
The 'inner' function can usually be found 'inside' (parenthesis), $\left|\text{ absolute value}\right|$ or $\sqrt{\text{square root}}$.

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

Refer to previous hints.