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

Question

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 *) — kirma, Jun 9, 2015 at 13:50
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. — MarcoB, Jun 9, 2015 at 14:00
@MarcoB thanks for taking the time to explain.. I am willing to learn :q — baloo, Jun 9, 2015 at 14:06

baloo · Accepted Answer · 2015-06-09 14:01:57Z

1

gaps[f_] := 
     Not[Reduce[
       Exists[{y}, Element[x, Reals] && y == f, Element[y, Reals]]]] 
    gaps[fuu[x]] // FullSimplify
    (*x == 0*)

answered Jun 9, 2015 at 14:01

baloo

991 silver badge8 bronze badges

$\begingroup$ now i feel stupid and smart at the same moment :3 lol $\endgroup$
– baloo
Jun 9, 2015 at 14:02
$\begingroup$ Thanks for posting the answer (+1) And hey, you solved your problem, nothing to feel stupid about there! :-) $\endgroup$
– MarcoB
Jun 9, 2015 at 14:09

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