There exists a function f(x) satisfying f(0) = 1, f'(0) = -1, f(x)>0 for all x and

JEE Advanced Mathematics question

There exists a function satisfying , , for all and

Answer: (A)

satisfies , , , and for all . So (a) is possible.

The others are impossible: in (b), (c), (d) we have

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Question ID VK-109233