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Discuss the continuity of the function f, where f is defined by

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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,...
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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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