Let f(x) be a continuous function such that f(x) does not vanish for all x R. If _2^3 f(x) ,dx= _ -2 ^3 f(x) ,dx then f(x), x R, is

JEE Advanced Mathematics question

Let be a continuous function such that does not vanish for all . If then , , is

Answer: (D)

Subtracting,

f dx- f dx= f(x) dx=0 .

This is a single condition on the values of in only. It is satisfied by the odd function , but also by the even function (since ), and by

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Question ID VK-109544