Suppose that $f$ is an invertible function from $(-\infty,\infty)$ to $(-\infty,\infty)$.  If $f(f(x))=x$, find $f(x)-f^{-1}(x)$.
I notice that the equation $f(f(x))=x$ implies that $f$ is its own inverse, that is, $f^{-1}(x)=f(x)$. Therefore, $f(x)-f^{-1}(x)=f(x)-f(x)=0$.

