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f (x + y) <=f (xy) for x,y reals

Source: Mathematics Regional Olympiad of Mexico Center Zone 2019 P2

November 14, 2021
inequalitiesFunctional inequalityfunctionalalgebra

Problem Statement

Find all functions f:R→R f: \mathbb {R} \rightarrow \mathbb {R} such that f(x+y)≤f(xy) f (x + y) \le f (xy) for every pair of real x x , y y.
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