Problem

Source: Turkey TST 2000

Tags: function, induction, algebra, inequalities, TST, additive function, functional equation



Given is a function f:RR such that |f(x+y)f(x)f(y)|1. Prove the existence of an additive function g:RR (that is g(x+y)=g(x)+g(y)) such that |f(x)g(x)|1 for any xR