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Math Help - Inverse Notation

  1. #1
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    Inverse Notation

    Express the following using inverse notation:


    (2)/(n+3)


    Now, I tried the problem treating it as a function, placing f(x)= in front of the equation. I solved it as I normally would to come out with the answer:


    f^(-1)(x)=-3+(2)/(n)


    But to my suprise, it was wrong. I double, triple, even quadruple checked, but every time it still came out as incorrect.


    This problem is part of a practice test, so I looked up the answer, to be:


    2(n+1)^(-1)


    I understand what they're asking for, just have no clue how to figure it thru. Any help is appreciated. If you have any questions, please feel free to ask. Thank you ahead of time!
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  2. #2
    MHF Contributor
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    Re: Inverse Notation

    Hey wuzimu69.

    Given y = 2/(x+3) to find the inverse we swap x and y and solve for our new y which gives:

    x = 2/(y+3)
    y + 3 = 2/x which means
    y = 2/x - 3

    Assume that the answer from the book is true. Then swap x and y to get the original function leaves us with:

    x = 2(y+1)^(-1)

    1/x = 1/2 * (y+1)
    1/x = 1/2*y + 1/2
    1/x - 1/2 = 1/2*y
    y = 2/x - 1 and grouping together gives us:

    y = (2-x)/x which is not our original function.

    In short: you are right and they are wrong.
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