MathNet 2011 Question 4

Let $f: \mathbb{R} \longrightarrow \mathbb{R}$ be a function such that $x f(y)=y f(x)$ for all $x, y \in \mathbb{R}$. Find the intersection of the graphs of $y=f(x)$ and $y=x^{2}+1$ if $f(1)=-1$.