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Math Help - Find inverse of a function

  1. #1
    Junior Member freestar's Avatar
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    Find inverse of a function

    y=\sqrt{x^2-2x}

    I figure the restriction on the domain would be x\geq2 or x\leq0

    x = \sqrt{y^2-2y}

    x^2 = y(y-2)

    It's driving me insane. How do I isolate the 'y'?!?
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Find inverse of a function

    Quadratic formula on y.
    y^ - 2y - x^2 = 0
    a = 1
    b = -2
    c = -x^2
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  3. #3
    MHF Contributor
    skeeter's Avatar
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    Re: Find inverse of a function

    Quote Originally Posted by freestar View Post
    y=\sqrt{x^2-2x}

    I figure the restriction on the domain would be x\geq2 or x\leq0

    x = \sqrt{y^2-2y}

    x^2 = y(y-2)

    It's driving me insane. How do I isolate the 'y'?!?
    x^2 = y^2 - 2y

    x^2 + 1 = y^2 - 2y + 1

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

    \pm \sqrt{x^2+1} = y - 1

    y = 1 \pm \sqrt{x^2+1}

    now all you have to do is figure out if its plus, or minus
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  4. #4
    Junior Member freestar's Avatar
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    Re: Find inverse of a function

    ahh completing the square. Thanks a lot!
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  5. #5
    Super Member TheChaz's Avatar
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    Re: Find inverse of a function

    Quote Originally Posted by freestar View Post
    ahh completing the square. And the quadratic formula works too! You guys are geniuses.
    Thanks a lot!
    I couldn't have said it better myself. You're welcome!
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