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Domain of a function

  1. Nov 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider some simple single-variable function such as
    f(x)=2x+1
    The domain,codomain and range of the above function is set of all real numbers.
    But why not the set of all complex numbers?
    if x = 3+4i
    f(x) = 6+8i + 1 = 7+8i,so it is possible for x to be a complex no?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 18, 2012 #2

    HallsofIvy

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    If your text book has not dealt with complex numbers, then the "default" number system is the set of real numbers. It really should be stated somewhere in your textbook, perhaps in the preface of first chapter, but not necessary with each problem.
     
  4. Nov 19, 2012 #3
    My book has mentioned complex no before,but the author still wrote down the domain is the set of all real numbers instead of complex numbers.
     

    Attached Files:

  5. Nov 19, 2012 #4

    symbolipoint

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    The range and domain are complex numbers a+bi for which b=0. Your function uses only Real Numbers.
     
  6. Nov 19, 2012 #5
    That means the range and domain of this function are the set of complex number?
     
  7. Nov 19, 2012 #6

    Mark44

    Staff: Mentor

    You attached an image of the problem solutions. How is the problem presented? There might be a clue that the author intended the domain to be the reals.
     
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