I interpreted the question myself from another angle: a circle is a function where every f(x) is an equal linear distance to an arbitrary fixed point z. So, the "inverse" to this function could be a function where every f(x) must have a different linear distance to z.

Yep, this would have the same effect. Both of these define all of the points that do not describe the circle.

However, as someone said above, f() is the inverse of g() if g(f(x)) = x. When put into practice, this means that the inverse is the reflection of the original function over y = x.

However, there's one problem with looking at the problem this way: A circle is NOT a function. Therefore, it does not have an inverse as we are thinking of it. A circle can be described by two functions, and both of these inverses combine to form the same circle. So, the inverse of a circle is (sort of) itself.