Question 13
Let $f: \mathbb{Q}^{+} \to \mathbb{R}^{+}$ be a function that satisfies
$$
f(x + y) - f(x - y) = 4\sqrt{f(x)f(y)}
$$
for all $0 \lt y \lt x$.
(a) Prove that $f(2x) = 4f(x)$ for all $x \in \mathbb{Q}^{+}$.
(b) Find all such functions.
$$
f(x + y) - f(x - y) = 4\sqrt{f(x)f(y)}
$$
for all $0 \lt y \lt x$.
(a) Prove that $f(2x) = 4f(x)$ for all $x \in \mathbb{Q}^{+}$.
(b) Find all such functions.