# Find all points of discontinuity of f where f is defined by'

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

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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.