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Math Help - Inverse function

  1. #1
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    Inverse function

    The problem is to find the inverse function of f expressed as f^-1(x).
    f(x)=x/(1+x).
    When i start to work on the problem i get stuck at
    x=f(y)=y/(1+y)
    x(1+y)=y
    And i dont see a way to get it to f-1(x).
    Somehow it should be f^-1(x)=x/(1-x).

    Thankful for any help.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    We have:

    y=\dfrac{x}{1+x}

    Solving:

    x=\dfrac{y}{1-y}=f^{-1}(y)

    Changing the name for the variable y:

    f^{-1}(x)=\dfrac{x}{1-x}


    Fernando Revilla
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  3. #3
    Junior Member BugzLooney's Avatar
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    How did you get to x=\dfrac{y}{1-y}?

    All I can get is x=y(1+x)
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  4. #4
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    When finding the inverse, replace the x's with y's and y's with x's and then isolate the y.

    \displaystyle y=\frac{x}{1+x}\Rightarrow x=\frac{y}{1+y}\Rightarrow x(1+y)=y\Rightarrow x=y-xy\Rightarrow x=y(1-x)\Rightarrow f^{-1}(x)=\frac{x}{1-x}
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