Question

Examine that sin |x| is a continuous function.

Answer 1

Let g(x) =|x| and h(x) = sin x

Now, g(x)=|x| is the absolute valued function, so it is continuous function for all $xϵR$
h(x) = sin x is the sine function, so it is continuous function for all $xϵR$

$\therefore$ (hog)(x)=h[g(x)]=h(|x|) = sin |x|

Since, g(x) and h(x) are both continuous functions for all $xϵR$ so, composition of g(x) and h(x) is also a continuous function for all $xϵR$
Thus, f(x) =sin |x| is a continuous function