Answer
Domain: all real numbers satisfy $x^{2}+y^{2}+z^{2}\ne0$
Range: $(0,\infty)$
Level surfaces: $f(x,y,z)=c$ (positive constant)
Work Step by Step
Function: $f(x,y,z)=\frac{1}{x^{2}+y^{2}+z^{2}}$
Domain: x, y, and z can be any real numbers except zeros at the same time, that is $x^{2}+y^{2}+z^{2}\ne0$
Range: $f(x,y,z)\gt0$
Level surfaces: $f(x,y,z)=c$ (positive constant)
$x^{2}+y^{2}+z^{2}=\frac{1}{c}$ represents a series of spheres.
For example, when $c=1$,
$x^{2}+y^{2}+z^{2}=1$ is a sphere shown in the figure.
