Question 91
Find all functions $f : \mathbb{R} \to \mathbb{R}$ that satisfy
$$
f(y^2f(x) - f(xy)) = f(y^2) + 2(x^2 - f(x))(f(y) - 1) + 1
$$
for all real numbers $x$ and $y$.
$$
f(y^2f(x) - f(xy)) = f(y^2) + 2(x^2 - f(x))(f(y) - 1) + 1
$$
for all real numbers $x$ and $y$.