Question 90
Let $\mathbb{R}^+$ be the set of all positive real numbers. Find all functions $f: \mathbb{R}^+ \to \mathbb{R}^+$ such that
$$
f(x + y^2 f(y)) = f(1 + y f(x)) f(x)
$$
for all positive real numbers $x, y$.
$$
f(x + y^2 f(y)) = f(1 + y f(x)) f(x)
$$
for all positive real numbers $x, y$.