MathDB
Almost symmetric functional equation in positive reals

Source: 2nd Memorial Mathematical Competition "Aleksandar Blazhevski - Cane" - Problem 6

January 12, 2021
algebrafunctional equation

Problem Statement

Let R+\mathbb{R}^{+} be the set of all positive real numbers. Find all the functions f:R+→R+f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+} such that for all x,y∈R+x, y \in \mathbb{R}^{+}, f(x)f(y)=f(y)f(xf(y))+1xy. f(x)f(y) = f(y)f(xf(y)) + \frac{1}{xy}.
Back to ProblemsView on AoPS