Examine that $\sin |x|$ is a continuous function.

Solution:

Let’s assume $f(x)=|x|$ and $g(x)=\sin x$, therefore

$($ gof $) x=g\{f(x)\}=g(|x|)=\sin |x|$

So now, $f$ and $g$ are continuous, as a result their composite, (gof) is also continuous.

As a result, $\sin |x|$ is continuous.