pre-calc

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find the inverse of the function


f(x) = x^2 − 6x, x ≥ 3

  • pre-calc -

    Your given function will be the part of the parabola which lies to the right of the vertex (3, -9)

    so y = x^2 - 6x
    inverse is
    x = y^2- 6y
    y^2 - 6y = x
    complete the square:
    y^2 - 6y+ 9 = x+9
    (y-3)^2= x+9
    y - 3= ± √(x+9)
    y = 3 ± √(x+9)

    but we only used the part for x≥3 of the original, so
    the inverse is
    f^-1 (x) = 3 + √(x+9) , x ≥ -9

    check:
    let x = 4
    f(4) = 16 - 24 = -8
    f^-1 (-8) = 3 + √(-8+9)
    = 3 + √1 = 4

    let x = 5.67
    f(5.67) = -1.8711
    f^-1 (-1.8711) = 3 + √(-1.8711+9)
    = 3+√7.1289
    =3 + 2.67
    = 5.67
    I am very confident my inverse is correct!

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