# Math Help - domain of f(x,y,z)

1. ## domain of f(x,y,z)

describe the domain of f(x,y,z) = sqrt(1-x^2-(y^2/9)-(z^2/4))

i feel as if its 1>= x^2-(y^2/9)-(z^2/4) but i am not sure...can any one help???

2. Originally Posted by chris25
describe the domain of f(x,y,z) = sqrt(1-x^2-(y^2/9)-(z^2/4))

i feel as if its 1>= x^2-(y^2/9)-(z^2/4) but i am not sure...can any one help???

Since the radicand needs to be positive we can se up the inequality

$1-x^2-\frac{y^2}{9}-\frac{z^2}{4} \ge 0 \iff x^2+\frac{y^2}{9}+\frac{z^2}{4} \le 1$

The domain is the surface and interior of an ellipseoid centered at the origin.