IMO Shortlist 2018 problem A5

Determine all functions $f:(0,\infty)\to\mathbb{R}$ satisfying $\left(x+\frac{1}{x}\right)f(y)=f(xy)+f\left(\frac{y}{x}\right)$ for all $x,y>0$ .

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf

Školjka