Question 21
Let $\mathbb{R}^+$ denote the set of all positive real numbers. Find all functions $f: \mathbb{R}^+ \to \mathbb{R}$ satisfying
$$
f(x) + f(y) \le \frac{f(x+y)}{2}, \quad \frac{f(x)}{x} + \frac{f(y)}{y} \ge \frac{f(x+y)}{x+y},
$$
for all $x, y \in \mathbb{R}^+$.
$$
f(x) + f(y) \le \frac{f(x+y)}{2}, \quad \frac{f(x)}{x} + \frac{f(y)}{y} \ge \frac{f(x+y)}{x+y},
$$
for all $x, y \in \mathbb{R}^+$.