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What's the inverse of f(x)= e^x/(1+2e^x)?

  1. Sep 8, 2008 #1
    What's the inverse of f(x)= e^x/(1+2e^x)?
     
  2. jcsd
  3. Sep 9, 2008 #2
    Hi, nfxgosu!

    You just have to solve for 'x':

    [tex]f(x)=y=\frac{e^x}{1+2e^x}[/tex]

    [tex](1+2e^x)y=e^x[/tex]

    [tex]y+2ye^x-e^x=0[/tex]

    [tex]e^x(2y-1)=-y[/tex]

    [tex]e^x=-\frac{y}{2y-1} /ln[/tex]

    [tex]x=\ln\frac{y}{1-2y}[/tex]

    So, for the inverse function we have:

    [tex]\overline{f}(x)=\ln\frac{x}{1-2x}[/tex]

    Best wishes, Marine
     
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