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March 29, 2017

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Find the inverse function of f

f(x) = x^2 + x, x >(or equal to) (-1/2)

Thanks!

  • Math - ,

    let y = x^2 + x , x ≤ -1/2
    the inverse is
    x = y^2 + y

    solving for y ...

    y^2 + y - x = 0
    y = (-1 ± √(1 - 4x))/2

    f(x) = -1/2 ± √(1-4x)/2 where x ≤ 1/4
    but in the original we are only considering the left "wing" of the parabola, so in the inverse we have to consider only
    f(x) = -1/2 - √(1-4x)/2 , for x ≤ 1/4

    testing:
    in original, let x = -5
    f(-5) = 25-5 = 20 , point is (-5,20)

    in the inverse
    f(20) = -1/2 - √81/2 = -1/ - 9/2 = -5

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