Question

Sin |x| is a continuous function for

Options

• x ∈ R

• x ∈ I

• x ∈ N

• None of these

Answer 1

x ∈ R

Explanation:

Let `g(x) = sin x, h(x) = |x|`

`(goh) (x) = g(h(x)) = g(|x|) = sin|x| = f(x)`

Now, `g(x) = sin x` and `h(x) = |x|`

Both are continuous for all x ∈ R.

∴ `f(x) = (goh) (x) = sin |x|` is continuous at all x ∈ R.