Let f(x)=x^5+2 e^ x / 4 for all x ∈ R . Consider a function g(x) such that (g f)(x)=x for all x ∈ R . Then the value of 8 g^ (2) is :

Correct answer: D. 16 aligned & f(x)=2 & when x=0 & g^ (f(x)) f^ (x)=1 & g^ (2)= 1 f^ (0) & f^ (x)=5 x^4+(2)/(4) e^ x / 4 & g^ (2)=2 & Ans =16 & Option (1) aligned

JEE Main 20244 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 4 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Differentiation

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Differentiation

Let f(x)=x^5+2 e^ x / 4 for all x ∈ R . Consider a function g(x)...

Let

f(x)=x^5+2 \mathrm{e}^{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}

. Then the value of

8 g^{\prime}(2)

is :

Options

Correct answer

D. 16

Step-by-step solution

\begin{aligned} & f(x)=2 \\ & \text{ when } x=0 \\ & \because g^{\prime}(f(x)) f^{\prime}(x)=1 \\ & g^{\prime}(2)=\frac{1}{f^{\prime}(0)} \\ & \because f^{\prime}(x)=5 x^4+\frac{2}{4} e^{x / 4} \\ & g^{\prime}(2)=2 \\ & \text{ Ans }=16 \\ & \text{ Option (1) }\end{aligned}

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