IrMO 2021 Problem 5

The function $g : [0, \infty) \to [0, \infty)$ satisfies the functional equation: $g(g(x)) = \frac{3x}{x + 3}$ , for all $x \ge 0$ . You are also told that for $2 \le x \le 3$ : $g(x) = \frac{x + 1}{2}$ . (a) Find $g(2021)$ . (b) Find $g(1/2021)$ .