For the function `f(x)=sin^(-1)(x^2-1)`
to be define, we will have to have `-1<=x^2-1<=1 =>`
`0<=x^2<=2 => -sqrt(2)<=x<=sqrt(2)`
Hence your domain is `[-sqrt2,sqrt2]`
As for your other question, in general `abs(x)<a => -a<x<a`
if you want to exclude zero from your answer, then you will obtain
`-a<x<0 or 0<x<a`
Which is not the case of this problem.