Let \alpha, \beta and \gamma be three positive real numbers. Let f(x)=\alpha x^5+\beta x^3+\gamma x, x \in R and g: R \to R. be such that g(f(x))=x for all x \in R. If {\a}_1, {\a}_2, {\a}_3, . . ., {\a}_{ {\n}} be in arithmetic progression with mean zero, then the value of f(g(\frac{1}{ {\n}} \sum_{i=1}^{ {\n}} f( {\a}_i))) is equal to: [28-Jul-2022-Shift-1]

JEE Mains 28-July-2022 Shift 1 Solved Paper

Section: Mathematics

Question : 18 of 90

Marks: +1, -0

Let α,β and γ be three positive real numbers. Let f(x)=αx5+βx3+γx,x∈R and g:R→R. be such that g(f(x))=x for all x∈R. If a1,a2,a3,...,an be in arithmetic progression with mean zero, then the value of f(g(‌

‌

∑

i=1

f(ai))) is equal to:

[28-Jul-2022-Shift-1]

Validate

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