Find all functions $f\colon \mathbb R \to \mathbb R$ such that $f(f(x)(y + 1)) = x[f(y) + 1]$, $\forall x, y \in \mathbb R$.
Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$