jmc

Applying $f^{-1}$ to both sides of the equation $f(f(x))=x$, we get $f^{-1}(f(f(x)))=f^{-1}(x)$. By definition of the inverse function, $f^{-1}(f(x))=x$, so $f^{-1}(f(f(x)))=f(x)$. Then $f(x)=f^{-1}(x)$, so $f(x)-f^{-1}(x)=\boxed{0}$.