Question

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

Answer 1

$f\left(x\right)=\sin \left(x\right)$

Let $g\left(x\right)=\sin x\&h\left(x\right)=\left(x\right)$

Go $h\left(x\right)=\sin \left(x\right)$

$=f\left(x\right)$

So $f\left(x\right)=$go $h\left(x\right)$

As g & h both are continuous

So is go $h\left(x\right)=f\left(x\right)$

Hence $f\left(x\right)$ is continuous.