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 ?
FunctionDomain[1/x, x, Reals] // FullSimplify
(* x != 0 *)
$\endgroup$