JEE Main 2022MathematicsDifferentiationEasyMCQ

JEE Main 2022 — Differentiation Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

Let f:R→R be defined as fx=x3+x-5. If gx is a function such that fgx=x,∀x∈R, then g'63 is equal to ______

Choose an option

Show full solutionCorrect option: B
Correct answer
B149

Step-by-step explanation

Here, gfx=x as fx and gx are inverse of each other.

Now, g'fxf'x=1

⇒g'fx=1f'x       …i

Now fx=63  ⇒ x3+x-5=63

⇒  x3+x-68=0

So x=4 satisfies the above equation

g'63=1f'4  from i

=1342+1=149

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About this question

This is a previous-year question from JEE Main 2022, 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.