Answer
The value of $f\left( 12 \right)-f\left( -12 \right)$ is $7$.
Work Step by Step
We have to compute the value of $f\left( 12 \right)$; put the value of $x$ (12) in the given function $x+3\text{ if }x\ge 5$ as given below:
$f\left( x \right)=x+3$
$\begin{align}
& f\left( 12 \right)=12+3 \\
& =15
\end{align}$
Now, to compute the value of $f\left( -12 \right)$, consider the given function $f\left( x \right)=8\text{ if }x<5$.
Therefore,
$f\left( -12 \right)=8$
Now, put the obtained values and compute the required value $f\left( 12 \right)-f\left( -12 \right)$ as given below:
$\begin{align}
& f\left( 12 \right)-f\left( -12 \right)=15-8 \\
& =7
\end{align}$
Thus, the value of $f\left( 12 \right)-f\left( -12 \right)$ is $7$.
