Answer
The functions from Exercise 87 and 88 both are inverses.
Work Step by Step
$h\left( x \right)=\frac{x}{2}+20$ and $d\left( x \right)=2\left( x-20 \right)$.
Evaluate the value of $\left( h\circ d \right)\left( x \right)$ as follows.
$\left( h\circ d \right)\left( x \right)=h\left( 2\left( x-20 \right) \right)$
Use the function $h\left( x \right)=\frac{x}{2}+20$ as follows.
$\left( h\circ d \right)\left( x \right)=\frac{2\left( x-20 \right)}{2}+20$
Use the function $d\left( x \right)=2\left( x-20 \right)$ as follows.
$\begin{align}
& \left( h\circ d \right)\left( x \right)=x-20+20 \\
& =x
\end{align}$
Thus, the value of $\left( h\circ d \right)\left( x \right)$ is x.
Evaluate the value of $\left( d\circ h \right)\left( x \right)$ as follows.
$\left( d\circ h \right)\left( x \right)=d\left( h\left( x \right) \right)$
Use the function $d\left( x \right)=2\left( x-20 \right)$ as follows.
$\left( d\circ h \right)\left( x \right)=d\left( \frac{x}{2}+20 \right)$
Use the function $h\left( x \right)=\frac{x}{2}+20$ as follows.
$\begin{align}
& \left( d\circ h \right)\left( x \right)=2\left( \frac{x}{2}+20-20 \right) \\
& =2\left( \frac{x}{2} \right) \\
& =x
\end{align}$
Thus, the value of $\left( d\circ h \right)\left( x \right)$ is x.
Therefore, $\left( h\circ d \right)\left( x \right)=\left( d\circ h \right)\left( x \right)=x$, so from the above mentioned definition it can be concluded that the functions $h\left( x \right)\text{ and }d\left( x \right)$ are inverse to each other.
