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JEE Main 2022 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 28 July 2022, Shift 1, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

Let

\alpha,\beta

and

\gamma

be three positive real numbers. Let

f(x)=\alpha x^5+\beta x^3+\gamma x,\ x\in\mathbf{R}

and

g:\mathbf{R}\to\mathbf{R}

be such that

g(f(x))=x

for all

x\in\mathbf{R}

. If

a_1,a_2,a_3,\ldots,a_n

be in arithmetic progression with mean zero, then the value of

f\left(g\left(\frac{1}{n}\sum_{i=1}^{n}f(a_i)\right)\right)

is equal to :

(1) $0$ Official answer
(2) $3$
(3) $9$
(4) $27$

Official answer

Option 1

NTA final key (2022 Session 2).

Chapter: Relations and Functions
Topic: No close match in our taxonomy
Idea tested: No close match in our taxonomy

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 42 of the 174 JEE Main shifts held from 2017 to 2026.