I'm quite confused by the function y = |x^2 - 1|

I understand that y = x^2 - 1 when x^2 - 1 > 0 etc

But how do you solve it?

You get x^2 - 1 > 0

x^2 > 1

x > + or - 1

but it should be x<-1 and x>1

Is there some sort of inequation sign change when one of the sides is square rooted? Thanks in advance :)