Find all points of discontinuity of f, where f is defined by - Maths - Continuity and Differentiability

Question

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

Gopal Mohanty · Accepted Answer

The given function f is

It is known that,

Therefore, the given function can be rewritten as

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 < 0 Case II: If c = 0, then the left hand limit of f at x = 0 is,

The right hand limit of f at x = 0 is,

It is observed that the left and right hand limit of f at x = 0 do not coincide Therefore, f is not continuous at x = 0 Case III:

Therefore, f is continuous at all points x, such that x > 0 Hence, x = 0 is the only point of discontinuity of f

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