Finding the range of this function of 2 variables:

[JC3187]

f(x,y) = ln(9 - x² - y²)

Domain I got:

(x, y) in R² such that x² + y² < 9

How do I find the range from the domain?

Wouldn't it be all positive numbers of ln such that it is less than ln(9)?

Answer says less than or equal to 9, I don't get why.

Any input is appreciated!

 

[maajdl]

Write the domain a little bit more precisely, and you will see why.

 

[JC3187]

Natural domain: 9 - x² - y² > 0
x² + y² < 9

How more precise can I be with this...

 

[maajdl]

0 <= x² + y² < 9

 

[JC3187]

Still am confused...
Why is it between 0 and 9?

 

[Mark44]

Still am confused...
Why is it between 0 and 9?

Because, for the natural log to be defined, x² + y² < 9,
but the smallest value of x² + y² is 0.
Therefore, you have 0 ≤ x² + y² < 9

 

[JC3187]

Things are now clear, Thank you all!