Find all points of discontinuity of f, where f is defined by

The given function is

We know that if x < 0

⇒ |x| = -x

So, we can rewrite the given function as:

⇒ f(x) = -1 for all x ϵ R

Let k be the point on a real line.

Then, f(k) = -1

= -1= f(k)

Thus,

Therefore, the given function is a continuous function.