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f (x + 1) >= f (x) + 1, f (x y) >=ge f (x)f (y)

Source: 2016 Saudi Arabia IMO TST , level 4+, II p2

July 29, 2020
algebraFunctional inequality

Problem Statement

Find all functions f:R→Rf : R \to R satisfying the conditions: 1. f(x+1)≥f(x)+1f (x + 1) \ge f (x) + 1 for all x∈Rx \in R 2. f(xy)≥f(x)f(y)f (x y) \ge f (x)f (y) for all x,y∈Rx, y \in R
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