MathDB
Proving existence of x,y such that f(x+y)<=f(x)(1+yf(x))

Source: Turkish NMO 1996, 6. Problem

July 31, 2011
functioninductionalgebra proposedalgebra

Problem Statement

Show that there is no function f:R+→R+f:{{\mathbb{R}}^{+}}\to {{\mathbb{R}}^{+}} such that f(x+y)>f(x)(1+yf(x))f(x+y)>f(x)(1+yf(x)) for all x,y∈R+x,y\in {{\mathbb{R}}^{+}}.
Back to ProblemsView on AoPS