A twist in your normal functional equations
Algebra
Level
5
Let \( \mathfrak{G} \) be the set of all functions \( f \) from the set of positive reals to the set of positive reals such that
\( f(3x) \geq f(f(2x)) + x, \ ∀ x \in \mathbb{R^{+}} \).
Find the maximum real number \( \mathfrak{k} \) such that for all such functions \( f \in \mathfrak{G} \), the following holds:
\( f(x) \geq \mathfrak{k} x \).
by
Anqi Li