Question

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

Answer 1

The given function f is 

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 < −3 Case II:

Therefore, f is continuous at x = −3
Case III:

Therefore, f is continuous in (−3, 3).
Case IV:

It is observed that the left and right hand limit of f at x = 3 do not coincide. Therefore, f is not continuous at x = 3 Case V:

Therefore, f is continuous at all points x, such that x > 3 Hence, x = 3 is the only point of discontinuity of f.