\item Obtain the one-to-one function $f_1$ and $f_2$ by cutting the graph of $f$ at 
      a certain point ($x_1$, $y_1$) so that domain of ($f_1$)=($-∞$ , $x_1$] and 
      domain ($f_2$)=[$x_1$,$+∞$)
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    You need \infty – percusse Sep 18 '13 at 15:00
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    When using XeLaTeX or LuaLaTeX as your typesetter, you need to include the »unicode-math« package. – Thorsten Donig Sep 18 '13 at 15:07
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    Just a general tip: It's safter to use \(f_1\) and \[f_1\] than $f_1$ and $$f_1$$. For more information, see this question: tex.stackexchange.com/questions/503/why-is-preferable-to or read about it in l2tabu. – Sam Whited Sep 18 '13 at 15:11
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    @SamWhited -- I would disagree with you on the claim that there's a generic safety related advantage to using \( ... \) rather than $ ... $ to delimit inline math. Indeed, since \(and \) are not "robust" commands (in the LaTeX sense of the word "robust"), it's perilous to use them in the arguments of "moving" commands; no such difficulties arise with $. Note that the link you provide regards the use of $$ -- a rather different matter. – Mico Sep 18 '13 at 15:58
  • @Mico Fair point; l2tabu doesn't mention \(\) either, though I had thought it talked about line spacing a bit. Oh well, ignore my comment (although I'd still go with the LaTeX way unless you need to put it in a moving argument for some reason). – Sam Whited Sep 18 '13 at 16:20

A better style is:

Obtain the one-to-one function $f_1$ and $f_2$ by cutting the graph of $f$ at a certain point $(x_1, y_1)$ so that domain of $(f_1)=(-\infty , x_1]$ and domain $(f_2)=[x_1,+\infty)$

(Please compare the obtained spacing).

| improve this answer | |

If you are still faced with such a problem, as the last resort, you can use the rotated eight as follows.

$(-\infinity, x_1]$

enter image description here

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  • Only meticulous readers will spot the difference. – kiss my armpit Sep 18 '13 at 15:38
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    Every good math font has the symbol corresponding to \infty. – egreg Sep 18 '13 at 15:44
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    @egreg: Yes. It is just for emergency purposes. :-) – kiss my armpit Sep 18 '13 at 15:47
  • Some fonts have a \infty that really looks like a rotated 8 instead of a distinct design. – lblb Oct 14 '17 at 15:48

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