Okay. Quite right about the Limit of the composite going to zero for x->0 (and going to 1 for x->1, for that matter). And, a simple plot of the the composite shows a straight line up through zero and 1 with not even a hiccup. I should have looked a little more carefully before I spoke.
However, what I noticed initially was that Mathematica encountered an infinite expression when I tried
Composition[f,f,f][x]/.x->0
It still gave me zero as the output (which I didn't notice at first), but I was focused on the infinite expression message as the reason that FunctionDomain gave me a discontinuous domain.
Well, obviously (perhaps), that's why "Reals" works as a domain quantifier in the above code. I think you gave me the answer to the problem I was working on. But why doesn't FunctionDomain work as a quantifier in this problem?
