MathDB

A4

Part of 2017-IMOC

Problems(1)

f(x+f(y))<=xf(y)+x over R, prove no solutions

Source: IMOC 2017 A4

8/12/2021
Show that for all non-constant functions f:Rā†’Rf:\mathbb R\to\mathbb R, there are two real numbers x,yx,y such that f(x+f(y))>xf(y)+x.f(x+f(y))>xf(y)+x.
fefunctional equationFunctional inequalityalgebra