Školjka

%V0 Let $\mathbb{R}^+$ be the set of all positive real numbers. Find all functions $f: \mathbb{R}^+ \longrightarrow \mathbb{R}^+$ that satisfy the following conditions: - $f(xyz)+f(x)+f(y)+f(z)=f(\sqrt{xy})f(\sqrt{yz})f(\sqrt{zx})$ for all $x,y,z\in\mathbb{R}^+$; - $f(x)<f(y)$ for all $1\le x<y$.