Functions with multiple variables

[Niles]

Homework Statement

I have a function f(x,y,z) = 1/(x^2+y^2+z^2). I have to find the domain.
It is R^3, but x^2+y^2+z^2 != 0. How do I write that and am I correct?

 

[fikus]

you're right. Think where are the points with x^2+y^2+z^2=0.
You can write the domain as: $$\mathbb{R}^3 \setminus{\{0,0,0\}}$$

 

[HallsofIvy]

Or:
$$\{ (x,y,z)| x^2+ y^2+ z^2\ne 0 \}$$