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A function is defined as follows:

Which one of the following is correct in respect of the above function?

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  1. f(x) is continuous at x = 0 but not differentiable at x = 0
  2. f(x) is continuous as well as differentiable at x = 0
  3. f(x) is discontinuous at x = 0
  4. None of the above

Answer (Detailed Solution Below)

Option 3 : f(x) is discontinuous at x = 0
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Detailed Solution

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Concept:

  • We say f(x) is continuous at x = c if

LHL = RHL = value of f(c) i.e., 

 

Calculation:

Given:  

                      (∵ |x| = -x, if x < 0)

                    (∵ |x| = x, if x > 0)

Here, LHL ≠ RHL, so f(x) is discontinuous.

Hence, option (3) is correct.

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