I think he'll still enjoy it with my shortcut guide rather than a long interactive guide. There are enough steps to fill in (and small pitfalls) to make it mathematically rigorous.Yes -- that's where I was heading. But I didn't want to "deprive" Shyan of the enjoyment I experienced (some time ago) of discovering these things by working them out.
Actually, one can do ##f=1/r## in an direct way by finding the implicit algebraic equation it satisfies in terms of ##x##, and proceeding similar to the case of the inverse of a polynomial. This is enjoyable, too, and one doesn't need limits. This works for any algebraic function, but not for exponentials, etc..