Investigate the continuity of a function I'm trying to determine whether the following function is continuous:
$y=\frac{1}{\sqrt{1+x}-\sqrt{1-x}}$. Imo it is continuous, because it is a composition of two continuous functions $y=\frac{1}{x}$ and $y=\sqrt{1+x}-\sqrt{1-x}$. 
So my answer is, that the function is continuous on it's domain and it's not continuous on $\mathbb{R}$. Am I correct?
Thanks

You are correct but a more detailed answer would explain the domain as well. 
The domain is $$[-\sqrt 2 /2,0)\cup (0, \sqrt 2/2]$$
