CAPS 2009 Problem 1

Let $\mathbb{R}^+$ denote the set of positive real numbers. Find all functions $f : \mathbb{R}^+\to\mathbb{R}^+$ that satisfy $$\Big(1+yf(x)\Big)\Big(1-yf(x+y)\Big)=1$$ for all $x,y\in\mathbb{R}^+$ .