Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ
Published on: August 12, 2026

If , then is

A
Continuous on [–1, 1] and differentiable on (–1, 1)
B
Continuous on [–1,1] and differentiable on (–1, 0) ∪ ∪ (0, 1)
C
Continuous and differentiable on [–1, 1]
D
None of these

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Text Solution

Verified by Experts
The correct answer is:
B

We have, . The domain of definition of is [–1, 1].

For we have

Since is not defined on the right side of and on the left side of . Also, when or . So, we check the differentiability at x = 0.

Now, (LHD at ) =

= =

Similarly, (RHD at x = 0) =

Hence, is not differentiable at x = 0.

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