JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

Let $\alpha, \beta$ and $\gamma$ be three positive real numbers. Let $f(x)=\alpha x^5+\beta x^3+\gamma x, x \in \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be such that $g(f(x))=x$ for all $x \in \mathbb{R}$. If $a_1, a_2, a_3, \ldots, a_n$ be in arithmetic progression mean is zero, then the value of $f\left(g\left(\frac{1}{n} \sum\limits_{i=1}^n f\left(a_i\right)\right)\right)$ is equal to