Answer
True.
Work Step by Step
Let $g(x) = |x|$.
$g(f(x)) = |f(x)|$
If $f(x)$ is continuous, and $g(x)$ is continuous, we know that $f(g(x))$ must be continuous, according to Theorem 9, which says that a continuous function of a continuous function is continuous.
We are told that $f(x)$ is continuous and we know that the function $|x|$ is continuous, therefore $g(f(x)) = |f(x)|$ must be continuous.
