Answer
See the explanation below.
Work Step by Step
(a)
Provided function $g\left( x \right)=\left\{ \begin{align}
& \sqrt{x-4}\text{ if }x\ge \text{4} \\
& 4-x\text{ if }x\text{ 4} \\
\end{align} \right.$.
To find $g\left( 13 \right)$, put $x=13$ in function $g\left( x \right)=\sqrt{x-4}$.
When $x\ge 4$,
$\begin{align}
& g\left( x \right)=\sqrt{x-4} \\
& g\left( 13 \right)=\sqrt{13-4} \\
& =\sqrt{9} \\
& =3.
\end{align}$
(b)
Let us consider the provided function $g\left( x \right)=\left\{ \begin{align}
& \sqrt{x-4}\text{ if }x\ge \text{4} \\
& 4-x\text{ if }x\text{ 4} \\
\end{align} \right.$.
To find $g\left( 0 \right),$ put $x=0$ in function $g\left( x \right)=4-x$.
When $x<4,$
$\begin{align}
& g\left( x \right)=4-x \\
& g\left( 0 \right)=4-0 \\
& =4
\end{align}$
(c)
Let us consider the provided function $g\left( x \right)=\left\{ \begin{align}
& \sqrt{x-4}\text{ if }x\ge \text{4} \\
& 4-x\text{ if }x\text{ 4} \\
\end{align} \right.$.
To find $g\left( -3 \right)$, put $x=-3$ in function $g\left( x \right)=4-x$.
When $x<4$,
$\begin{align}
& g\left( x \right)=4-x \\
& g\left( -3 \right)=4-\left( -3 \right) \\
& =7
\end{align}$
