i tried to find domain of inverse function of f(x)= (sin^-1)*(x^2-1)... but  how does 0< lxl <root2 change to (-root2,0) U (0,root2)??

Expert Answers
rcmath eNotes educator| Certified Educator

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.