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g (1990) =? if g (x) <=x, g (x + y) <=g (x) + g (y) (Chile NMO 1990 P4)

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November 20, 2021
algebrafunctional

Problem Statement

The function gg, with domain and real numbers, fulfills the following: ∙\bullet g(x)≤xg (x) \le x, for all real xx ∙\bullet g(x+y)≤g(x)+g(y)g (x + y) \le g (x) + g (y) for all real x,yx,y Find g(1990)g (1990).
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