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B Range of function

  1. Jul 18, 2016 #1
    Hello,
    This is a very basic question but bothering me on some exercises.
    upload_2016-7-19_0-14-33.png , upload_2016-7-19_0-14-33.png
    Then how is the range of y is upload_2016-7-19_0-15-49.png ? What if x is 0, then we can have y = 1 or y = -1.
    While doing some exercises I encountered this issue and can't match the answers.
    Thanks in advance
     
  2. jcsd
  3. Jul 18, 2016 #2
    For the most part, ##\sqrt{x}## indicates the positive square root value.

    Since, in this case, y is a function, there is not the slightest ambiguity. Functions are only allowed to have one value for any one input. So ##y=\sqrt{1-x^2}## refers only to the positive root.
     
  4. Jul 18, 2016 #3

    fresh_42

    Staff: Mentor

    If you just write ##y = \sqrt{1-x^2}## then it is only the positive root. Otherwise you should write ##y = ± \sqrt{1-x^2}## to indicate that you consider both roots. And even this is a bit sloppy because it means ##y \in \{ ± \sqrt{1-x^2} \}##. I normally write ##y_{1,2} = ± \sqrt{1-x^2}##.
     
  5. Jul 18, 2016 #4
    The function part made it clear. Thanks.
     
  6. Jul 18, 2016 #5

    Erland

    User Avatar
    Science Advisor

    But the range isn't ##y\ge 0##. It's ##0\le y\le 1##.
     
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