MathDB

f(f(x) + y) = ax + 1/f (1/y) , when x,y >0

Source: 49th Austrian Mathematical Olympiad National Competition (Final Round, part 2) 31st May 2018 p1

May 25, 2019

algebrafunctional equation

Problem Statement

Let

a \ne 0

be a real number. Find all functions

f : R_{>0}\to R_{>0}

with

f(f(x) + y) = ax + \frac{1}{f\left(\frac{1}{y}\right)}

for all

x, y \in R_{>0}

.
(Proposed by Walther Janous)