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Math Help - Please find this inverse function

  1. #1
    Newbie petike's Avatar
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    Exclamation Please find this inverse function

    Hi all,
    could anybody find inverse function to this function:

    <br />
f(x) = \frac{2x}{1 - x^2}<br />

    Please write here the whole solution.

    Thanks in advance.
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  2. #2
    A riddle wrapped in an enigma
    masters's Avatar
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    Quote Originally Posted by petike View Post
    Hi all,
    could anybody find inverse function to this function:

    <br />
f(x) = \frac{2x}{1 - x^2}<br />

    Please write here the whole solution.

    Thanks in advance.
    A few have looked at this, but no takers. Let's see if I can get this thing started. First restate the function with y, then interchange the x and y.

    y = \frac{2x}{1 - x^2}

    x = \frac{2y}{1 - y^2}

    x(1-y^2)=2y

    x-xy^2=2y

    -xy^2+x-2y=0

    xy^2+2y=x

    y^2+\frac{2}{x}y=1

    Complete the square on the left

    y^2+\frac{2}{x}y+\left(\frac{1}{x}\right)^2=1+\fra  c{1}{x^2}

    \left(y+\frac{1}{x}\right)^2=\frac{x^2+1}{x^2}

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

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

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

    What do you think?
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  3. #3
    Newbie petike's Avatar
    Joined
    Oct 2008
    Posts
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    Thumbs up Soluted

    Oh,
    thaaank you very much.
    You have really helped me.

    You've got my thanks.
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