Finding the domain for a rational function.

[cavalieregi]

Hi I have the function

I have worked out the domain as not equal to 1 using the fact the denominator can't equal 0. Now I am stuck finding the range. How would I find it without graphing. The answer is y<0 , y=>3.

 

[jbunniii]

Hi I have the function
View attachment 70478

I have worked out the domain as not equal to 1 using the fact the denominator can't equal 0.

There's one more value of $x$ which must be excluded.

Now I am stuck finding the range. How would I find it without graphing. The answer is y<0 , y=>3.

After excluding $1-x^2 = 0$, you are left with either $1 - x^2 < 0$ or $1 - x^2 > 0$. Try writing these inequalities in terms of $x$ instead of $x^2$.