Answer
Domain: all real numbers
Range: $0\lt f(x,y,z)\leq1$
Level surfaces: $f(x,y,z)=c$ (constant in $(0,1]$)
Work Step by Step
Function: $f(x,y,z)=\frac{1}{x^{2}+y^{2}+z^{2}+1}$
Domain: x, y, and z can be any real numbers
Range: $0\lt f(x,y,z)\leq1$
Level surfaces: $f(x,y,z)=c$ (constant in $(0,1]$)
$x^{2}+y^{2}+z^{2}=\frac{1}{c}-1$ represents a series of spheres.
For example, when $c=\frac{1}{2}$,
$x^{2}+y^{2}+z^{2}=1$ is a sphere shown in the figure.
