Lambda the Ultimate

I am reading Hutton's book, programming in Haskell, and got stumped by a question. redefine map f using foldr. Since foldr is described as replacing (:) in a list with some provided operator it seemed it shouldn't be too hard.
foldr requires two components a what to do on empty list and the operator.

So I tried this:

> folmap :: (a -> b) -> [a] -> [b]
> folmap f = foldr (:.f) []

My reasoning is that you apply the : operator after f on every value in the list. (Though I may not understand the (.) I was thinking that if f = (a ->b) and g = (b -> c) then g.f would be g performed after f (or g.f is f followed by g).

Any advice??