Verified Solution • 2025–26 Session moderate

QJEEM20Ma2656: JEE Main 2020 Mathematics - Class 12 JEEM20Ma2656 Solution: Let ƒ and g be differentiable functions on R such that fog is…

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

Multiple Choice Options

  • A 1
  • B 5
  • C 25{2 \over 5}
  • D 15{1 \over 5}

Step-by-Step Verified Solution

Given the function composition f(g(x)) is the identity function, it means f(g(x)) = x for all x.

⇒\Rightarrow ƒ'(g(x)) g'(x) = 1

put x = a

⇒\Rightarrow ƒ'(b) g'(a) = 1

⇒\Rightarrow ƒ'(b) = 15{1 \over 5}

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