Question 77
Let $D := \mathbb{R} \setminus \{0,1\}$. Find all functions $f:D \rightarrow D$ which satisfy for any $x, y \in \mathbb{R}$ with $x, xy \in D$ the equation
$$
f(f(xy)) = 1 - \frac{1}{y f(f(f(x)))}
$$
$$
f(f(xy)) = 1 - \frac{1}{y f(f(f(x)))}
$$