MathDB
Cute functional system

Source: 2020 1st OMpD L3 P4 - Brazil - Olimpíada Matemáticos por Diversão

July 8, 2023
functionreal numberpositive realalgebra

Problem Statement

Let R+\mathbb{R}^+ the set of positive real numbers. Determine all the functions f,g:R+→R+f, g: \mathbb{R}^+ \rightarrow \mathbb{R}^+ such that, for all positive real numbers x,yx, y we have that f(x+g(y))=f(x+y)+g(y) and g(x+f(y))=g(x+y)+f(y)f(x + g(y)) = f(x + y) + g(y) \text{ and } g(x + f(y)) = g(x + y) + f(y)
Back to ProblemsView on AoPS