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Discuss the continuity of the function f, where f is defined by
Asked by Vruthi Last Modified
Answer The given function f is
The given function is defined at all 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:
The left hand limit of f at x = −1 is,
The right hand limit of f at x = −1 is,
Therefore, f is continuous at x = −1
Case III:
Therefore, f is continuous at all points of the interval (−1, 1).
Case IV:
The left hand limit of f at x = 1 is,
The right hand limit of f at x = 1 is,
Therefore, f is continuous at x = 2
Case V:
Therefore, f is continuous at all points x, such that x > 1
Thus, from the above observations, it can be concluded that f is continuous at all points of the real line.
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