## Calculus (3rd Edition)

The function $|g(x)|$ acts like the function $|x|$.
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 $g(x)$.