### Home > APCALC > Chapter 4 > Lesson 4.1.3 > Problem4-35

4-35.

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

1. $y=\sin\left(x^2\right)$

$x^2$ is the inner function. $\sin\left(x\right)$ is the outer function.

$y = f\left(g\left(x\right)\right)$

2. $y=\sin^2\left(x\right)$

$x^2$ is the outer function. What is the inner function?

3. $y=\csc\left(x\right)$

Recall that $y=\csc\left(x\right)$ is the reciprocal of $y=\sin\left(x\right)$.

4. $y = \operatorname { csc } ^ { 2 } ( \frac { 1 } { x } )$

Refer to the hint in part (c).