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Math Help - Taking the inverse of a function

  1. #1
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    Dec 2007
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    Taking the inverse of a function

    So I forget how to find the inverse of a function.
    The function I have is f(x) = 3x^2 - x .
    I remember that I have to switch the x and y points so that it looks like this
    x = 3y^2 - y but I'm not sure how to solve it.
    Thanks
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    1,092
    Quote Originally Posted by the-G View Post
    So I forget how to find the inverse of a function.
    The function I have is f(x) = 3x^2 - x .
    I remember that I have to switch the x and y points so that it looks like this
    x = 3y^2 - y but I'm not sure how to solve it.
    Thanks
    You need to complete the square. First take \frac{x}{3} = y^2 - \frac{y}{3} and then add \frac{1}{36} to both sides of the equation to get \frac{x}{3} + \frac{1}{36} = y^2 - \frac{y}{3} + \frac{1}{36}.

    Then we have completed the square:

    \frac{x}{3} + \frac{1}{36} = (y - \frac{1}{6})^2.

    Can you finish it from there?
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