I have doubt ! regarding to [this question](https://math.stackexchange.com/questions/1453187/function-fx-x-1-3-please-check-whether-my-solution-is-correct) , 

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> 
> Is this function $f(x)=x^{-1/3}$ continuous, when $x$ varies from $-1$
>  to $1?$
> 
> 
> 

[![enter image description here](https://i.stack.imgur.com/CaPjl.png)](https://i.stack.imgur.com/CaPjl.png)

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As I read, when left limit is not equivalent to right limit ,then function is not continuous . For this function $f(x)=x^{-1/3}$ should not be continuous , since it's undefined at $x=0$ , [check-here](http://www.themathpage.com/acalc/continuous-function.htm#cont) or [here](http://www.mathsisfun.com/calculus/continuity.html)