Find the domain of the function $w=f(x,y,z)=\sqrt{x^{2}+y^{2}+z^{2}-1}$ and graph the domain.

Solution  Since the expression under the radical must be nonnegative, the domain of $f$ consists of all points for which $x^{2}+y^{2}+z^{2}-1\geq 0.$ The domain is the set of all points on and outside of the unit sphere $x^{2}+y^{2}+z^{2}=1$; that is, the set $\{ (x,y,z) \,|\,x^{2}+y^{2}+z^{2}\geq 1\}$. See Figure 5.