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Math Help - Composition of functions equation, please help anyone?

  1. #1
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    Composition of functions equation, please help anyone?

    Thanks a bunch!
    Last edited by bxuan; September 16th 2012 at 05:07 PM. Reason: Solved
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  2. #2
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    Re: Composition of functions equation, please help anyone?

    f(x) is quadratic ...

    f(x) = ax^2 + bx + c

    f(2x-3) = a(2x-3)^2 + b(2x-3) + c = x^2 + x - 1

    f(2x-3) = a(4x^2-12x+9) + b(2x-3) + c = x^2 + x - 1

    4ax^2 + (2b-12a)x + (9a-3b+c) = x^2 + x - 1

    equate coefficients ...

    4a = 1 ... a = \frac{1}{4}

    2b - 3 = 1 ... b = 2

    \frac{9}{4} - 6 + c = -1 ... c = \frac{11}{4}

    f(x) = \frac{x^2}{4} + 2x + \frac{11}{4}
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