### Home > APCALC > Chapter 4 > Lesson 4.2.1 > Problem4-49

4-49.

Given each function $h$ below, define functions $f$ and $g$ so that $h\left(x\right) = f\left(g\left(x\right)\right)$. (Note: $f\left(x\right) ≠ x$ and $g\left(x\right) ≠ x$)

1. $h(x)=$$\sqrt{\sin(x^2)+1}$

One possible solution is:
$g\left(x\right) = x^{2}$

$f(x)=\sqrt{\text{sin}x+1}$

Find another possible solution.

2. $h\left(x\right)=$$\left(3x^3-12\right)^2+2$

One possible solution is:
$g\left(x\right) = 3x^{3}$
$f\left(x\right) = \left(x − 12\right)^{2} + 2$
Find another possible solution.