A Dream Within a Dream

★ 7/10functions AM-GM Functional Equations

Problem

A function $f(x)$ is strictly decreasing on $(0, +\infty)$ , and for every $x \in (0, +\infty)$ ,

f(x) \cdot f\!\left(f(x) + \frac{2}{x}\right) = \frac{1}{3}.

Let $g(x) = f(x) + 4x^2$ . Find the minimum value of $g(x)$ .

Answer

Solution

Difficulty	7/10
Topics	functions, AM-GM, Functional Equations

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