<s>[INST] Domain of $f(x,y) = {\sqrt{x+y-1 \over x-y+1}}$ How I can get the domain of the function
$$ f(x,y) = \sqrt{x+y-1 \over x-y+1}?$$
I know that is: $x+1 \neq y$ and $x^2 \ge (y-1)^2$
But I don't know how to get the second condition.
 [/INST] Hint: Where defined, $f(x,y)$ equals
$$f(x,y)=\sqrt{\frac{x+y-1}{x-y+1}\cdot\frac{x-y+1}{x-y+1}}=\frac{\sqrt{(x+(y-1))\cdot(x-(y-1))}}{|x-y+1|}=\frac{\sqrt{x^2-(y-1)^2}}{|x-y+1|}. $$
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