Let f: R R be a function such that f(x + y) = f(x) + f(y), , x, y R . If f(x) is differentiable at x = 0 then

JEE Advanced Mathematics question

Let be a function such that , . If is differentiable at then

Answer: (B),(C)

Putting : . For any ,

f'(x) = = = = f'(0),

and this limit exists because is differentiable at 0. So is differentiable at **every** with , a

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Question ID VK-110802