The given function f is defined at all the points of the real line. Let c be a point on the real line.

**Case I:**

Therefore, f is continuous at all points x, such that x < 2

**Case II:**

Therefore, f is continuous at x = 2

**Case III:**

Therefore, f is continuous at all points x, such that x > 2

Thus, the given function f is continuous at every point on the real line.

Hence, f has no point of discontinuity.