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11 October, 04:28

Let g (x) = x+2. Find f (x) if f (x) is a quadratic function of the form f (x) = ax^2+bx+c and f (g (x)) = 2x^2-x+3

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  1. 11 October, 05:48
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    Let g (x) = x + 2

    f (g (x)) = 2x^2 - x + 3

    = 2 (x^2 - x/2 + 3/2)

    =2 (x^2 + 4x + 4) - 9x - 5

    =2 (x+2) ^2 - 9 (x+5/9)

    =2 (x + 2) ^2 - 9 (x + 2) + 13

    f (x) = 2x^2 - 9x + 13
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