Range of a function question

[bobbarkernar]

Homework Statement

Let f(x,y,z)=e^sqrt(z-5x^2-5y^2), find the domain and range of this function

Homework Equations

The Attempt at a Solution

ok i know how to get the domain of the function:
you cant take the sqrt of a negative number you set up the inequality
z-5x^2-5y^2>= 0 and solve for z and you find that z>=5x^2+5y^2

my question is about the range im not sure how to find it. is it like in 2d all possible numbers in the y, but in 3d its all numbers in z??

thank you

 

[gammamcc]

Do it in pieces:

What is the desired range of z-5x^2-5y^2?
What then is the range of h=\sqrt{z-5x^2-5y^2}?
That being the domain of e^h here, what range results?