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Homework Help: Confused about +- symbol use in inverse function

  1. Jun 20, 2012 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

    Hi, so this isn't a question, it's just an example that they've given, but I don't understand the explanation given.

    You have :

    y = x^2 - 4
    x = y^2 - 4
    y^2 = x + 4
    y = ± sqrt(x+4)

    I don't get why there is a ± symbol there. My book says that it's necessary because there are two values for y that will satisfy the equation, and that if x = 0, y could be +2 or -2.

    I understand that y could = +2, because sqrt 4 = +2, but I don't see how it could equal -2.

    How would I know that I should include the ± symbol in front of the sqrt(x+4)? Thanks
  2. jcsd
  3. Jun 20, 2012 #2

    Ray Vickson

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    What is (-2)*(-2)?

  4. Jun 20, 2012 #3
    Whenever you take the square root of something it requires a +or- because the square of either the negative or positive value of that term would yield the same number when it is squared. for instance (-x)^2=(x)^2

    since you are squaring y, you must be aware that the sqrt of (x+4) will net y regardless if it is positive or negative
  5. Jun 20, 2012 #4
    AHHHH! I get it.

    This forum rocks, thanks!
  6. Jun 20, 2012 #5
    indeed it does
  7. Jun 21, 2012 #6


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    Note, by the way, that what this is saying is that the original function does NOT HAVE an inverse! A function has an inverse if and only if it is "one to one". That is, there is only one value of x that gives a specific y value. It that is not true, we can choose a specific one of the x values for a given y value, as here choosing "+" or "-", which is equivalent to choosing a subset of the original function.
  8. Jun 21, 2012 #7
    For example, if you have ##p^2=2##, then ##p=\pm\sqrt2##. Same thing here.
    Last edited: Jun 21, 2012
  9. Jun 21, 2012 #8
    ±√2 that is
  10. Jun 21, 2012 #9
    Oops, sorry about that. Editted.
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