Question 86
Let $\mathbb{R}_+$ be the set of positive real numbers. Find all functions $f : \mathbb{R}_+ \to \mathbb{R}_+$ such that
$$
f(xy + x + y) + f\left(\frac{1}{x}\right) f\left(\frac{1}{y}\right) = 1
$$
for every $x, y \in \mathbb{R}_+$.
$$
f(xy + x + y) + f\left(\frac{1}{x}\right) f\left(\frac{1}{y}\right) = 1
$$
for every $x, y \in \mathbb{R}_+$.