KöMaL problem A, 2017

Algebra Difficulty 6.0 National Olympiad Find the answer Hungary

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

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