Multivariable Calculus: How to conclude the domain for x and y? I am self-learning multivariable calculus for the first time, and I have this practice problem that I am not sure if my understanding is correct.
Suppose I have a multivariable function defined as $f(x,y)$ = $x^2$ + $y^2$, and its domain is D = {(x, y) s.t. $x^2$ + $y^2$$\le$1}.
I want to found out the domain for x and y individually.
I am not sure if I am correct, but I think in this case, the domain for x and y should be x $\in$ [0, 1] and y $\in$ [0, 1] since their sum can't be greater than 1.
Is my understanding correct in this case?

As @KaviRamaMurthy said, they can also take negative value.
As @TheoC. said, they can't simultaneously take numbers that $x^2+y^2>1$
In fact the domain of each of them is what "KaviRamaMurthy" said. But as they aren't independent variables, so when you choose one (foe example $x=t$) the other domain restricted ($y=\pm\sqrt{1-t^2}$).
