CPM Homework Help : CALC Problem 4-35

Given $f(x) =\operatorname{sin }x$ , $g(x) = x^2$ and $h ( x ) = \frac { 1 } { x }$ , use compositions to express each of the following functions.

$y =\operatorname{sin}(x^2)$
Hint (a):
$x^²$ is the inner function. $\operatorname{sin}(x)$ is the outer function.
Answer (a):
$y = f(g(x))$

$y =\operatorname{sin}^2(x)$
Hint (b):
$x^²$ is the outer function. What is the inner function?

$y =\operatorname{csc}(x)$
Hint (c):
Recall that $y =\operatorname{csc}(x)$ is the reciprocal of $y =\operatorname{sin}(x)$ .

$y = \operatorname { csc } ^ { 2 } ( \frac { 1 } { x } )$
Hint (d):
Refer to the hint in part (c).