Range of a function question

  • #1

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
 

Answers and Replies

  • #2
150
0
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?
 

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