Let f be a real-valued function defined on the interval (-1, 1) such that e^ -x f(x) = 2 + _0^x t^4 + 1 ,dt, for all x (-1, 1), and let f^ -1 be the inverse function of f. Then (f^ -1 )'(2) is equal to

JEE Advanced 2010 Mathematics question

Let f be a real-valued function defined on the interval such that , for all , and let be the inverse function of f. Then is equal to

Answer: (B)

Put : , so . Differentiate the given relation using the Leibniz rule: . At : .

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Question ID VK-025839