Question 153
Let $\mathbb{R}^+$ be the set of all positive real numbers. Find all functions $f: \mathbb{R}^+ \to \mathbb{R}^+$ satisfying
$$
(1 + y f(x))(1 - y f(x + y)) = 1
$$
for any $x, y \in \mathbb{R}^+$.
$$
(1 + y f(x))(1 - y f(x + y)) = 1
$$
for any $x, y \in \mathbb{R}^+$.