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g(g(x)) = 3x/(x + 3) for x>=0, g(x) = (x + 1)/2 for 2<=x<=3

Source: 2021 Irish Mathematical Olympiad P5

May 30, 2021
algebrafunctionalfunctional equation

Problem Statement

The function g:[0,∞)→[0,∞)g : [0, \infty) \to [0, \infty) satisfies the functional equation: g(g(x))=3xx+3g(g(x)) = \frac{3x}{x + 3}, for all x≥0x \ge 0. You are also told that for 2≤x≤32 \le x \le 3: g(x)=x+12g(x) = \frac{x + 1}{2}. (a) Find g(2021)g(2021). (b) Find g(1/2021)g(1/2021).
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