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Romania NMO 2022 Grade 11 P3

Source: Romania National Olympiad 2022

April 20, 2022
romaniacalculusfunctionFunctional inequality

Problem Statement

Determine all functions f:R→Rf:\mathbb{R}\to\mathbb{R} which are differentiable in 00 and satisfy the following inequality for all real numbers x,yx,y f(x+y)+f(xy)≥f(x)+f(y).f(x+y)+f(xy)\geq f(x)+f(y).Dan Ștefan Marinescu and Mihai Piticari
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