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Domain and range of a function of several variables

  1. Sep 13, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the domain and range of the following function:
    f(x, y) = ln(x+y)
    2. Relevant equations


    3. The attempt at a solution
    I know that the natural log ln(x) is only defined when x>0, so does that mean that ln(x+y) is only defined when x+y>0? Also, would the range just be all positive real numbers? Thanks
     
  2. jcsd
  3. Sep 13, 2015 #2

    Mark44

    Staff: Mentor

    Yes.
    Do you understand what this set looks like in the plane?
    No. What's the range of y = ln(x)? Is it just the positive reals?
     
  4. Sep 13, 2015 #3
    I don't understand what the set looks like in the plane. The range of ln(x) would be all real numbers, since it has an asymptote at y=0 where is approaches -∞, and approaches ∞ as x approaches ∞.
     
  5. Sep 13, 2015 #4

    Mark44

    Staff: Mentor

    Can you graph the inequality ##x + y \ge 0##?
    If not, graph the line x + y = 0. The inequality will be one side or the other of that line. Surely you must have done some graphing of inequalities in the past.
     
  6. Sep 13, 2015 #5
    I see what you're saying. Regarding the range, however, would it simply be all real numbers due to the range of ln(x) being all real numbers?
     
  7. Sep 13, 2015 #6

    Mark44

    Staff: Mentor

    Yes.
     
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