[tex]\it i)\ \begin{cases} \it x^2-1>0 \Rightarrow x^2>1 \Rightarrow \sqrt{x^2}>\sqrt 1 \Rightarrow |x|>1 \Rightarrow x\in\mathbb{R}\setminus[-1,\ \ 1]\\ \\ \it x^2-1\ne1 \Rightarrow x^2\ne2 \Rightarrow x\ne\pm\sqrt2\end{cases}\ \ \Rightarrow \\ \\ \\ \Rightarrow x\in(-\infty,\ -\sqrt2)\cup(-\sqrt2,\ -1)\cup(1,\ \sqrt2)\cup(\sqrt2,\ \infty)[/tex]
