Mathematics · Methods of Differentiation

JEE Main 2024 — 4 April, Shift 1 — Question 19

Let $f(\mathrm{x})=\mathrm{x}^{5}+2 \mathrm{e}^{\mathrm{x} / 4}$ for all $\mathrm{x} \in$ R. Consider a function $g(x)$ such that (gof) $(x)=x$ for all $x \in R$ . Then the value of $8 \mathrm{~g}^{\prime}(2)$ is :

Option A:
16
Correct
Option B:
4
Option C:
8
Option D:
2

Answer: A

Step-by-step solution

$f(x)=2$ when $\mathrm{x}=0$

$\because g^{\prime}(f(x)) f^{\prime}(x)=1$

$\mathrm{g}^{\prime}(2)=\frac{1}{\mathrm{f}^{\prime}(0)}$

$\because f^{\prime}(\mathrm{x})=5 \mathrm{x}^{4}+\frac{2}{4} \mathrm{e}^{\mathrm{x} / 4}$

$g^{\prime}(2)=2$

Ans $=16$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Mathematics
Chapter: Methods of Differentiation
Topic: First, second, third derivative of inverse of a function