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

4-49.

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

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

One possible solution is:
$g(x) = x^2$
$f(x)=\sqrt{\text{sin}x+1}$
Find another possible solution.

1. $h(x) = (3x^3 − 12)^2 + 2$

One possible solution is:
$g(x) = 3x^3$
f$(x) = (x-12)^2 + 2$
Find another possible solution.