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Finding the range of this function of 2 variables:

  1. Apr 12, 2014 #1
    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!
     
  2. jcsd
  3. Apr 12, 2014 #2

    maajdl

    User Avatar
    Gold Member

    Write the domain a little bit more precisely, and you will see why.
     
  4. Apr 12, 2014 #3
    Natural domain: 9 - x2 - y2 > 0
    x2 + y2 < 9

    How more precise can I be with this...
     
  5. Apr 12, 2014 #4

    maajdl

    User Avatar
    Gold Member

    0 <= x² + y² < 9
     
  6. Apr 12, 2014 #5
    Still am confused...
    Why is it between 0 and 9?
     
  7. Apr 12, 2014 #6

    Mark44

    Staff: Mentor

    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
     
  8. Apr 12, 2014 #7
    Things are now clear, Thank you all!
     
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