Pseudo

Find all functions $f:\mathbb{R}^+\to\mathbb{R}^+$ satisfying

$$ f(1+xy)=f(y)f(x+f(y)) $$

for all $x,y\in\mathbb{R}^+$. Provide and prove your answer in the following section.

Submit

The contest ended at 8:16 p.m. AEST on Thursday 2nd July. All submissions will be unofficial .