The domain of the derivative of the functions f(x) = cases ^ -1 x, & if |x| 1 1 2 (|x|-1), & if |x| > 1 cases is given by

MHT CET 2022 Mathematics question

The domain of the derivative of the functions is given by

(A)
(B)
(C)Correct
(D)

Answer: (C)

Solution

On each of and the function is a standard differentiable expression, so only need checking. At : but , so is discontinuous at and hence not differentiable there. At :

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Question ID VK-094466