1. ## define the domian

I'm having problems definning the value of the function with absoute value on top:

|x^2-1|/x^2-1

for the interval -1<x<1

because the square root of 1 is +1 or -1 , how do you define which value to
use in the above interval?

Because for x>=+1,-1 and x<+1,-1

2. ## Re: define the domian

I'm not sure what you are asking exactly. I'll try to help though.

The domain only depends on the denominator of that fraction, since the absolute value doesn't have any restriction as to what values of x you can put in it. But for the denominator:

$x^2-1\neq 0$
$x\neq \pm1$

So the domain of the function is $D=\left \{ x\in \mathbb{R} ~|~x\neq \pm 1 \right \}$

I'm also not sure what you mean when you say you can't find the value of the function for the interval (-1,1). Just put in a value, say x=0. And you get y=-1. That is the value of the function in the interval.