Question 50
Let $f: \mathbb{R}^+ \to \mathbb{R}^+$ be a function satisfying
$$
(f(xy))^2 = f(x^2)f(y^2)
$$
for all $x, y \in \mathbb{R}^+$ with $x^2y^3 \gt 2008$.
Prove that $(f(xy))^2 = f(x^2)f(y^2)$ for all $x, y \in \mathbb{R}^+$.
$$
(f(xy))^2 = f(x^2)f(y^2)
$$
for all $x, y \in \mathbb{R}^+$ with $x^2y^3 \gt 2008$.
Prove that $(f(xy))^2 = f(x^2)f(y^2)$ for all $x, y \in \mathbb{R}^+$.