# Functions with multiple variables

1. Sep 29, 2007

### Niles

1. The problem statement, all variables and given/known data

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?

2. Sep 29, 2007

### fikus

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

3. Sep 29, 2007

### HallsofIvy

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