Question 54
Find all functions $f: \mathbb{R} \setminus \{1\} \to \mathbb{R} \setminus \{0\}$ which satisfy the equations $f(0) = 1$ and $f(f(xy)) = 1 - \frac{1}{y f(f(f(x)))}$ for any real numbers $x$ and $y$ such that $xy \neq 0,\ xy \neq 1$ and $x \neq 1$.