JEE Main 2020 — Differentiation Question with Solution
From: JEE Main 2020 (Online) 9th January Evening Slot
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 :
Choose an option
Show full solutionCorrect option: D
Correct answer
D
Step-by-step explanation
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) =
ƒ'(g(x)) g'(x) = 1
put x = a
ƒ'(b) g'(a) = 1
ƒ'(b) =
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Differentiation chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2020, covering the Differentiation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.