Question 2
Find all functions $f \colon \mathbb{R}^+ \to \mathbb{R}^+$ such that for each $x \in \mathbb{R}^+$, there is exactly one $y \in \mathbb{R}^+$ satisfying $$
xf(y)+yf(x) \leq 2.
$$ Here $\mathbb R^+$ denotes the set of positive real numbers.
xf(y)+yf(x) \leq 2.
$$ Here $\mathbb R^+$ denotes the set of positive real numbers.