Examine that | x | is a continuous function. - Vidyadip

Question

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

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Answer

Let $f\left( x \right) = \left| x \right|$ and $g\left( x \right) = \sin \left| x \right|$, then

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

Now, f and g being continuous, it follows that their composite, (gof) is continuous.

Therefore, $\sin \left| x \right|$ is continuous.

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