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Math Help - Finding a Function's Inverse

  1. #1
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    Finding a Function's Inverse

    f(x) = 2(x - 1)^2 - 3
    f(x) = (2x - 2)^2 - 3
    (2x - 2)^2 = x + 3
    2x - 2 = \pm \sqrt{x + 3}
    2x = \pm \sqrt{\frac{x + 3}{2}}
    x = \pm \sqrt{\frac{x + 3}{2}} + 2
    f^-(x) = \pm \sqrt{\frac{x + 3}{2}} + 2

    That's how I solved it, but my textbook answer is
    f^-(x) = 1 \pm \sqrt{\frac{x + 3}{2}}

    Where was my error?
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  2. #2
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    Quote Originally Posted by shadow6 View Post
    f(x) = 2(x - 1)^2 - 3
    f(x) = (2x - 2)^2 - 3 mistake in going from above line to here.

    \textcolor{red}{2(x-1)^2 \ne (2x-2)^2}

    Where was my error?
    ...
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