1

Problems(1)

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

a \ne 0

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

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

x, y \in R_{>0}