Let $f:\mathbf{R}\to\mathbf{R}$ be defined as $f(x)=x^3+x-5$ If $g(x)$ is a function such that $f(g(x))=x$, $\forall$ 'x' $\in \mathbf{R}$, then $g'(63)$ is equal to __________.

JEE Main 2022 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 25 June 2022, Shift 1, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A.

Let

f:\mathbf{R}\to\mathbf{R}

be defined as

f(x)=x^3+x-5

g(x)

is a function such that

f(g(x))=x

\forall

'x'

\in \mathbf{R}

, then

g'(63)

is equal to __________.

(1) $\frac{1}{49}$ Official answer
(2) $\frac{3}{49}$
(3) $\frac{43}{49}$
(4) $\frac{91}{49}$

Official answer

Option 1

NTA final key.

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: Derivative of Inverse Functions via Chain Rule

Same idea in other shifts

Asked 4× in all

4 Apr 2024, Shift 1 · Q11Let $f(x)=x^5+2e^{x/4}$ for all $x \in \mathbf{R}$ . Consider a function $g(x)$ such that $(g\circ f)(x)=x$ for all $x \in \mathbf{R}$ .…MediumSingle correct
5 Apr 2024, Shift 1 · Q8Let $f(x)=x^5+2x^3+3x+1$ , $x\in\mathbb{R}$ , and $g(x)$ be a function such that $g(f(x))=x$ for all $x\in\mathbb{R}$ . Then…MediumSingle correct
9 Jan 2020, Shift 2 · Q60Let $f$ and $g$ be differentiable functions on $\mathbf{R}$ such that $f\circ g$ is the identity function. If for some $a,b\in\mathbf{R}$ ,…EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.