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Find all points of discontinuity of f, where f is defined by
Asked by Ankita Last Modified
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.
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