# Find the domain of the function

1. Feb 24, 2016

### says

1. The problem statement, all variables and given/known data
Find domain of f(x, y) = ln ((x2+2x+y2) / (x2−2x+y2))

2. Relevant equations

3. The attempt at a solution
Because the function is a natural ln, the restriction on the function is that everything inside the brackets has to >0, otherwise the function is undefined.

I worked on the problem for a while but wasn't getting anywhere so i plugged the equation into wolfram and got the domain { (x,y) ∈ R2 | 4x2 < (x2 + y2)2}

I'm not sure how to get there though...

[(x2+2x+y2) / (x2−2x+y2)] > 0

2. Feb 24, 2016

### Staff: Mentor

Because of the natural log, $\frac{x^2 + 2x + y^2}{x^2 - 2x + y^2}$ has to be positive, but you're forgetting that there is a restriction on the denominator.

3. Feb 24, 2016

### PeroK

First, note that for a fixed $y$ you have two quadratics in $x$. Perhaps start by analysing those quadratics.

4. Feb 24, 2016

### Ray Vickson

So, if $(x^2+2x+y^2)/(x^2-2x+y^2)>0$, then the numerator and denominator must both be > 0 or both be < 0. It might help to look at those two cases separately.