Answer
Domain = $\{(x,y,z)|\quad x^{2}+y^{2}+z^{2}\leq 1\}$
(see image)
Work Step by Step
Restriction on the square root: f is defined only for
$1-x^{2}-y^{2}-z^{2}\geq 0,$
$x^{2}+y^{2}+z^{2}\leq 1$
which is the region in $\mathbb{R}^{3}$, inside or on the sphere of radius 1, centered at the origin.
Domain = $\{(x,y,z)|\quad x^{2}+y^{2}+z^{2}\leq 1\}$
(see image)
