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    geobeeker's Avatar
    geobeeker Posts: 6, Reputation: 1
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    #1

    Dec 6, 2007, 07:15 AM
    complicated radical equation
    I know how to invert simple functions and how to solve simple radical equations, but this problem stumps me:

    find the inverse of y = f(x) = sqrt(x) / (x-1)

    Thank you.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Dec 6, 2007, 10:30 AM
    Try this: square your original equation to get:

    y^2 = x/(x^2-2x+1)

    Multiply through:
    y^2x^2 - (2y^2+1)x +y^2 = 0

    Apply the quadratic formula to solve for x, and you get:
    x = (2y^2 +1 +/- sqrt(4y^2+1))/(2y^2)

    Now check: in the original equation if x = 4, then y = sqrt(4)/(4-1) = 2/3. Plug 2/3 into the above for y and you get x = 4 or 1/4, so it works.

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