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Challenge problem to the community - - - domain and range

  1. Dec 14, 2011 #1
    What are the domain and range of the following:
    (Note: It is a relation that is not a function.)



    [itex]y^2(x^2 - 1) = x^4[/itex]
     
  2. jcsd
  3. Dec 14, 2011 #2

    dextercioby

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    Since there's no one to one correspondence between a value for x and a value for y, you have 2 different mappings (functions in their own right). y_1 (x) and y_2 (x) with the same maximal domain (R-{+-1}). y_1 is minus 1 times y_2, for any allowable value of x.
     
  4. Dec 14, 2011 #3
    .



    I take it you are only addressing the domain . . . for now.


    With your notation, does (R - {+-1}) mean [itex](-\infty, -1) \ \ \cup \ \ (-1, 1) \ \ \cup \ \ (1, \infty) \ ?[/itex]


    Or, does it mean [itex](-\infty, -1) \ \ \cup \ \ (1, \infty) \ ?[/itex]



    I am asking you for your clarification before I comment further on the
    possible/alleged correctness of your take on it. (I want to comment,
    but I am waiting on some more information.)
     
  5. Dec 15, 2011 #4

    dextercioby

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    I was too lazy to write down the LaTex code, but here goes

    [tex] \mathbb{R} - \{\pm 1\} [/tex].
     
  6. Dec 15, 2011 #5

    What about x = -1/2 or x = 1/2, for instance?


    Would those work or not?
     
  7. Dec 15, 2011 #6

    dextercioby

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    No, y would be imaginary.
     
  8. Dec 15, 2011 #7
    So, then, we must eliminate the first choice of interval notation
    in the above quote box. Is the second choice of interval notation
    in the quote box correct?


    Can x = 0 give y as a real value or not?
     
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