Question 45
Find all functions $f : \mathbb{Q}^+ \to \mathbb{R}^+$ such that
$$
f(xy) = f(x + y)(f(x) + f(y)), \text{ for any } x, y \in \mathbb{Q}^{+}.
$$
$$
f(xy) = f(x + y)(f(x) + f(y)), \text{ for any } x, y \in \mathbb{Q}^{+}.
$$
MathNet 2014 Question 45
Math Olympiad Vault · MathNet 2014