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Romanian District Olympiad 2019 - Grade 10 - Problem 1

Source: Romanian District Olympiad 2019 - Grade 10 - Problem 1

March 17, 2019
functionFunctional inequalityalgebra

Problem Statement

Find the functions f:R→(0,∞)f: \mathbb{R} \to (0, \infty) which satisfy 2−x−y≤f(x)f(y)(x2+1)(y2+1)≤f(x+y)(x+y)2+1,2^{-x-y} \le \frac{f(x)f(y)}{(x^2+1)(y^2+1)} \le \frac{f(x+y)}{(x+y)^2+1}, for all x,y∈R.x,y \in \mathbb{R}.
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