How to find all gaps of a domain of a function with Mathematica 9?

I tried it liek this:

My test-function:

fuu[x_] := Expand[FullSimplify[1/x]]


how i find the domain:

domain[f_] :=
Module[{},
Reduce[Exists[{y}, Element[x, Reals] && y == f, Element[y, Reals]]]]
domain[fuu[x]]
(*x < 0 || x > 0*)


How i tried to find the gaps:

gaps[f_] :=
Not[Reduce[
Exists[{y}, Element[x, Reals] && y == f, Element[y, Reals]]]]
gaps[fuu[x]]
(*! (x < 0 || x > 0)*)


How can i do it that he just says x == 0 ?

• In v10: FunctionDomain[1/x, x, Reals] // FullSimplify (* x != 0 *) Commented Jun 9, 2015 at 13:50
• I have Mathematica 9.. Commented Jun 9, 2015 at 13:53
• lol i just needed to Fullsimplify the last one.. Commented Jun 9, 2015 at 13:56
• sudo, rather than adding the answer to your question, would you mind posting it as an actual answer and in due time accepting it? That would make the question show up as answered, and it is encouraged on stackexchange to answer your own questions when you can. Commented Jun 9, 2015 at 14:00
• @MarcoB thanks for taking the time to explain.. I am willing to learn :q Commented Jun 9, 2015 at 14:06

gaps[f_] :=