What is the range of the function f(x,y,z)=e^sqrt(z-5x^2-5y^2)?

[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 can't 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 I am 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?