Question 94
Determine all the real-valued functions $f$ defined on the real line, for which the following identity is satisfied for any pair of real numbers $x, y$:
$$
f(f(x) - f(y)) = f(f(x)) - 2x^2f(y) + f(y^2).
$$
$$
f(f(x) - f(y)) = f(f(x)) - 2x^2f(y) + f(y^2).
$$