Question

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

Answer 1

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.