Maths Olympiad Prep

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Algebra Difficulty 6.0 National Olympiad Find the answer Hungary

Do there exist bijective functions f,g ⁣:QQf,g\colon \mathbb{Q}\to\mathbb{Q} such that the function f(g(x))f\big(g(x)\big) is strictly increasing, but the function g(f(x))g\big(f(x)\big) is strictly decreasing?

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