Answer
The function $|g(x)|$ acts like the function $|x|$.
Work Step by Step
We are given:
$f(x)=|g(x)|$
Rewrite the function:
$f(x)=\begin{cases}
-g(x),\text{ for }g(x)\leq 0\\
g(x),\text{ for }g(x)>0
\end{cases}$
Because $g(x)$ is continuous, $f(x)$ is continuous in the intervals for which $g(x)\not=0$. In the points in which $g(x)=0$, $f(x)$ is also continuous due to the continuity of $g(x)$.
Therefore the function $f$ is continuous on the domain of $g(x)$.
