Checking Continuity of functions Consider a function $\sqrt {x-1}$+$\sqrt{1-x}$.From here we can see that domain of the function is just 1 and range is 0.Still the function is continious at x=1 even though RHL and LHL limit doesn't exist. Can you guys tell me how this is possible. What is the criterion for checking continuity of functions 

What is your definition for $l=\lim\limits_{x\to 1}f(x)$ if it exists?
If this is it:
$$\forall\varepsilon>0,\exists\delta>0,\forall x\in D_f,|x-1|<\delta\implies|f(x)-f(1)|<\varepsilon$$
then  take ANY $\varepsilon>0$ and ANY $\delta>0$. $D_f=\{1\}$ so $|x-1|=0$ for any $x\in D_f$ and thus $f(x)=f(1)$.
