Question 82
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that the following equation holds for all $x, y \in \mathbb{R}$
$$
f\left(f(x)-y^{2}\right)=f(x)^{2}-2 f(x) y^{2}+f(f(y))
$$
$$
f\left(f(x)-y^{2}\right)=f(x)^{2}-2 f(x) y^{2}+f(f(y))
$$