Answer
a) 12
b) 5
c) 10
Work Step by Step
(a)
As $7\ne 5$.
So, the first part of the piecewise function will be applicable for $x=7$.
$\begin{align}
& h\left( x \right)=\frac{{{x}^{2}}-25}{x-5} \\
& h\left( 7 \right)=\frac{{{7}^{2}}-25}{7-5} \\
& h\left( 7 \right)=\frac{24}{2} \\
& h\left( 7 \right)=12
\end{align}$
Hence, the value of $h\left( 7 \right)$ is $12$.
(b)
As $0\ne 5$.
So, the first part of the piecewise function will be applicable for $x=0$.
$\begin{align}
& h\left( x \right)=\frac{{{x}^{2}}-25}{x-5} \\
& h\left( 0 \right)=\frac{{{0}^{2}}-25}{0-5} \\
& h\left( 0 \right)=\frac{-25}{-5} \\
& h\left( 0 \right)=5
\end{align}$
Hence, the value of $h\left( 0 \right)$ is $5$.
(c)
As $5=5$.
So, the second part of the piecewise function will be applicable for $x=5$.
$\begin{align}
& h\left( x \right)=10 \\
& h\left( 5 \right)=10
\end{align}$
Hence, the value of $h\left( 5 \right)$ is $10$.
