Question 79
Let $\mathbb{R}$ denote the set of all real numbers. Determine all functions $f: \mathbb{R} \setminus \{-1\} \to \mathbb{R}$ such that for all real numbers $x, y$ satisfying $(x+1)(y+1)(xy+1) \neq 0$, the equation
$$
f(x) f\left(f\left(\frac{1-y}{1+y}\right)\right) = f\left(\frac{x+y}{xy+1}\right)
$$
holds.
$$
f(x) f\left(f\left(\frac{1-y}{1+y}\right)\right) = f\left(\frac{x+y}{xy+1}\right)
$$
holds.