I'm not very good at math. So treat this post accordingly.
[Ooops! As Kevin points out. I meant the *inverse* function theorem. I did say I was no good at math. I've edited it now. Can't find the strikeout function.].
The basic idea here seems rather obvious. But I don't remember anyone making this connection before. Between the inverse function theorem and the choice of monetary policy instrument.
There's something in math called the Inverse Function Theorem. It says that if Y is a function of X then, under certain conditions, there must exist some inverse function such that X is a function of Y. If Y=F(X), then X=F-1(Y).