The function `f(x) =sin|x|` is continuous for all x

Explanation

`f(x) =sin|x|`

Let `g(x)=sinx` & `h(x)=|x|`

Now,
`goh(x)`
`=g(h(x))`
`=g(|x|)`

`=sin|x|`
`=f(x)`

Hence, `f(x)=goh(x)`

We know that
`g(x)=sinx` is continuous as `sinx` is always continuous
& `h(x)=|x|` is continuous as modulus function is continuous.

Hence, `g(x)` & `h(x)` are both continuous.

We know that
If two function of `g(x)` & `h(x)` are both continuous,
then their composition goh(x) is also continuous.

Hence, `f(x) =sin|x|` is continuous.