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A function f is defined by f:x→x+10 over x-8,x not equal to 8.Find
the values of x for which f^-1(x)=x.

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asked by mandy
  1. remember how I did the last one for you?

    original:
    y = (x+10)/(x-8)

    inverse:
    x = (y+10)/(y-8)
    xy - 8x = y+10
    xy - y = 8x + 10
    y(x-1) = (8x+10)/(x-1)

    f^-1 (x) = (8x+10)/(x-1)

    so we want:
    (8x+10)/(x-1) = x
    x^2 - x = 8x + 10
    x^2 - 9x - 10 = 0
    (x-10)(x+1) = 0
    x = 10 or x = -1

    check:
    f^-1 (10) = (80+10)/(10-1) = 90/9 = 10
    f^-1 (-1) = (-8+10)/(-1-1) = 2/-2 = -1

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    posted by Reiny

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