JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 18

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 $f\left(g\left(\dfrac1n\displaystyle\sum_{i=1}^nf(a_i)\right)\right)$ is equal to :