Question 79
Let $F$ be the set of all functions $f: \mathbb{R}^+ \to \mathbb{R}^+$ satisfying the condition
$f(3x) \geq f(f(2x)) + x$ for every real positive number $x$.
Find the greatest real number $\alpha$ such that for all $f \in F$, we have
$$
f(x) \geq \alpha x
$$
for every real positive number $x$.
$f(3x) \geq f(f(2x)) + x$ for every real positive number $x$.
Find the greatest real number $\alpha$ such that for all $f \in F$, we have
$$
f(x) \geq \alpha x
$$
for every real positive number $x$.