Answer
a)The value of $h\left( 5 \right)$ is $8$.
b)The value of $h\left( 0 \right)$ is $3$.
c)The value of $h\left( 3 \right)$ is $6$.
Work Step by Step
(a)
As $5\ne 3$.
So, the first part of the piecewise function will be applicable for $x=5$.
$\begin{align}
& h\left( x \right)=\frac{{{x}^{2}}-9}{x-3} \\
& h\left( 5 \right)=\frac{{{5}^{2}}-9}{5-3} \\
& h\left( 5 \right)=\frac{16}{2} \\
& h\left( 5 \right)=8
\end{align}$
Hence, the value of $h\left( 5 \right)$ is $8$.
(b)
As $0\ne 3$.
So, the first part of the piecewise function will be applicable for $x=0$.
$\begin{align}
& h\left( x \right)=\frac{{{x}^{2}}-9}{x-3} \\
& h\left( 0 \right)=\frac{{{0}^{2}}-9}{0-3} \\
& h\left( 0 \right)=\frac{-9}{-3} \\
& h\left( 0 \right)=3
\end{align}$
Hence, the value of $h\left( 0 \right)$ is $3$.
(c)
As $3=3$.
So, the second part of the piecewise function will be applicable for $x=3$.
$\begin{align}
& h\left( x \right)=6 \\
& h\left( 3 \right)=6
\end{align}$
Hence, the value of $h\left( 3 \right)$ is $6$.
