Question

What is the natural domain of the function f(x,y)=√(x^2-y^2 )?

Answer 1

Since $x^2-y^2\geq 0$ , it follows that $x^2 \geq y^2$ , that is, $|x| \geq |y|$ . This domain is contained between lines $y=-x$ and $y=x$ if $x \geq 0$, and between lines $y=x$ and $y=-x$ if $x<0$ , including these lines.