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Math Help - Inverse of Quadratic Function?

  1. #1
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    Inverse of Quadratic Function?

    Hi - I guess this is easy but I am having trouble solving it. I am supposed to find the inverse of the quadratic function

    y = x^2 - 2x +1

    Thanks in advance for any help, I am not sure if I can just factor it? The answer is supposed to be y = 1 +- srqrt X
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  2. #2
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    Quote Originally Posted by fumanchu View Post
    Hi - I guess this is easy but I am having trouble solving it. I am supposed to find the inverse of the quadratic function

    y = x^2 - 2x +1

    Thanks in advance for any help, I am not sure if I can just factor it? The answer is supposed to be y = 1 +- srqrt X
    You start by substituting x with y:

    x = y^2 - 2y + 1. Now we want to express y in terms of x. So, factor the polynomial:

    x = (y-1)^2.

    Therefore, y-1 = +-SQRT(x), so y = 1 +- SQRT(x).
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  3. #3
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    Thanks sorry I didn't get it at first.

    Do you know of a place that explains why the x ends up as + or - sqrt(x) when you take the square root. I understand that is the answer but I don't really get why. Sorry again.
    Last edited by mr fantastic; March 30th 2009 at 10:08 PM. Reason: Merged posts
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  4. #4
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    Quote Originally Posted by fumanchu View Post
    Do you know of a place that explains why the x ends up as + or - sqrt(x) when you take the square root. I understand that is the answer but I don't really get why. Sorry again.
    this is so because whwn u mutiply a neg. no. by itself(-a*-a) the result will come positive.
    and if u multiply a positive no. with itself(a*a) the result will be positive.
    so it cant be made out if the sqrt was originally posit. or neg.. so to be on the safer side we take both +&-.
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  5. #5
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    Quote Originally Posted by fumanchu View Post
    Do you know of a place that explains why the x ends up as + or - sqrt(x) when you take the square root.
    You get the "plus-minus" from the Quadratic Formula or, if you prefer, from completing the square. (But that's the hard way!)

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  6. #6
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    Wait, that can't be the inverse function. When you have the plus-minus sign, you have a one-to-many relation, so it is not a function! The exercise must give the original's function domain and codomain if you are expected to find its inverse.
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  7. #7
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    But the exercise, as originally posted, did not ask for an inverse function; it asked only for "the inverse". The "plus-minus" relation fulfills that requirement.
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  8. #8
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    Well, I suppose this is just semantics and is really irrelevant, but the OP did say "find the inverse of the quadratic function" and the inverse of a function must also be a function. So it must be asking the inverse function.
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  9. #9
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    Quote Originally Posted by Referos View Post
    ...the inverse of a function must also be a function.
    No; only some functions are "invertible"; only some functions have inverses which are also themselves functions. Usually, the inverse is just a "relation".
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