Question 35
Let $\mathbb{R}_+ = (0, \infty)$. Determine all functions $f : \mathbb{R}_+ \to \mathbb{R}_+$ such that
$$
f(xf(y)) + f(yf(z)) + f(zf(x)) = xy + yz + zx,
$$
for all $x, y, z \in \mathbb{R}_+$.
$$
f(xf(y)) + f(yf(z)) + f(zf(x)) = xy + yz + zx,
$$
for all $x, y, z \in \mathbb{R}_+$.