Question

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, .....a_n be in arithmetic progression with mean zero, then the value of \(f(g(\frac{1}{n}\displaystyle\sum_{i=1}^{n}f(a_ i)))\) is equal to :

(A) 0 

(B) 3 

(C) 9 

(D) 27

Answer 1

Correct option is (A) 0 

Consider a case when α = β = 0 then