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Functions question

2022 · 28 Jul · Shift 1 · Q36

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PYQ Library
JEE Main
Mathematics
Functions
2022 · 28 Jul · Shift 1 · Q36

Functions question

2022 · 28 Jul · Shift 1 · Q36

JEE MainMathematicsFunctionsMCQ+4 / −1

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} \rightarrow \mathbf{R}

be such that

g(f(x))=x

for all

x \in \mathbf{R}

. If

\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots, \mathrm{a}_{\mathrm{n}}

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

f\left(g\left(\frac{1}{\mathrm{n}} \sum\limits_{i=1}^{\mathrm{n}} f\left(\mathrm{a}_{i}\right)\right)\right)

is equal to :

A
0
B
3
C
9
D
27

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