control difference of inverses of two functions

Question

Let $f$ and $g$ be smooth functions from $\mathbb{R}$ to itself. How to express $f^{-1}(0)-g^{-1}(0)$ in terms of $f$ and $g$? Preferably, in terms of $f-g$. Here $f^{-1}$ means the inverse function. The motivation for my question is that I want to control $f^{-1}(0)-g^{-1}(0)$ under the assumption $f$ and $g$ are very close in some sense.