Let f(x) = cases (x - 1) ( 1 x - 1 ), & if x 1 0, & if x = 1 cases . Then which one of the following is true?

JEE Main 2008 Mathematics question

Let . Then which one of the following is true?

Answer: (3)

Near x = 0, f is a composition of differentiable functions (x − 1 ≠ 0), so it is differentiable at x = 0. At x = 1: , which has no limit as , so f is

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Question ID VK-039097