Question 72
A function $f$ defined on the set of real numbers $\mathbb{R}$ and taking nonnegative real values satisfies the condition
$$
f(x + y) \le 2 \max\{f(x), f(y)\}
$$
for all $x, y \in \mathbb{R}$. Is it true that for each positive integer $k$ the inequality
$$
f(x_1 + \cdots + x_k) \le 2(f(x_1) + \cdots + f(x_k))
$$
holds for all $x_1, \dots, x_k \in \mathbb{R}$?
$$
f(x + y) \le 2 \max\{f(x), f(y)\}
$$
for all $x, y \in \mathbb{R}$. Is it true that for each positive integer $k$ the inequality
$$
f(x_1 + \cdots + x_k) \le 2(f(x_1) + \cdots + f(x_k))
$$
holds for all $x_1, \dots, x_k \in \mathbb{R}$?