1
$\begingroup$

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 ?

$\endgroup$
5
  • $\begingroup$ In v10: FunctionDomain[1/x, x, Reals] // FullSimplify (* x != 0 *) $\endgroup$
    – kirma
    Commented Jun 9, 2015 at 13:50
  • $\begingroup$ I have Mathematica 9.. $\endgroup$
    – baloo
    Commented Jun 9, 2015 at 13:53
  • 1
    $\begingroup$ lol i just needed to Fullsimplify the last one.. $\endgroup$
    – baloo
    Commented Jun 9, 2015 at 13:56
  • 2
    $\begingroup$ 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. $\endgroup$
    – MarcoB
    Commented Jun 9, 2015 at 14:00
  • $\begingroup$ @MarcoB thanks for taking the time to explain.. I am willing to learn :q $\endgroup$
    – baloo
    Commented Jun 9, 2015 at 14:06

1 Answer 1

1
$\begingroup$
gaps[f_] := 
     Not[Reduce[
       Exists[{y}, Element[x, Reals] && y == f, Element[y, Reals]]]] 
    gaps[fuu[x]] // FullSimplify
    (*x == 0*)
$\endgroup$
2
  • $\begingroup$ now i feel stupid and smart at the same moment :3 lol $\endgroup$
    – baloo
    Commented 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
    Commented Jun 9, 2015 at 14:09

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