Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a,

Q: JEE Main 2023 Differentiation: Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, ...

The correct answer is A. Given the function composition f(g(x)) is the identity function, it means f(g(x)) = x for all x. ƒ'(g(x)) g'(x) = 1 put x = a ƒ'(b) g'(a) = 1 ƒ'(b) =

Question

Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, b R, g'(a) = 5 and g(a) = b, then ƒ'(b) is equal to :

Accepted Answer

Given the function composition f(g(x)) is the identity function, it means f(g(x)) = x for all x. ƒ'(g(x)) g'(x) = 1 put x = a ƒ'(b) g'(a) = 1 ƒ'(b) =

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1

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5

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