# 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:

$$f(x) \geq \mathfrak{k} x$$.

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