MathNet 2004 — Part 01 Question 192

Let $f$: $\mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(0) = 1$ and for any $x$, $y \in \mathbb{R}$, $f(xy+1) = f(x)f(y) - f(y) - x + 2$ holds. Then $f(x) = \underline{\hspace{2cm}}$.