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 < 1 

Case II:

Therefore, f is continuous at x = 1
Case III:

Therefore, f is continuous at all points x, such that x > 1 

Hence, the given function f has no point of discontinuity.