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Math Help - Inverse of a function

  1. #1
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    Inverse of a function

    Find the inverse of f(x)= x/(x+1)


    I have no idea where to begin. Everything I've tried just takes me back to the original problem.
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  2. #2
    Super Member 11rdc11's Avatar
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    y = \frac{x}{x+1}

    Swap x and y and slove for y

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

    x(y+1) =y

    xy +x -y = 0

    xy -y = -x

    y(x-1) = -x

    f^{-1}(x)=\frac{-x}{x-1}
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  3. #3
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    Quote Originally Posted by The Box View Post
    Find the inverse of f(x)= x/(x+1)


    I have no idea where to begin. Everything I've tried just takes me back to the original problem.
     f\left( x \right) = \frac{x}<br />
{{x + 1}} \hfill \\

     {\text{Let,  }}y = \frac{x}<br />
{{x + 1}} \hfill \\

    {\text{For finding inverse, interchange }}x{\text{ and }}y{\text{, and solve for y}} \hfill \\

      \Rightarrow x = \frac{y}<br />
{{y + 1}} \hfill \\

     \Rightarrow x\left( {y + 1} \right) = y \hfill \\

     \Rightarrow xy + x = y \hfill \\

    \Rightarrow x = y - xy \hfill \\

    \Rightarrow x = y\left( {1 - x} \right) \hfill \\

    \Rightarrow y = \frac{x}<br />
{{1 - x}} \hfill \\

     \Rightarrow f^{ - 1} \left( x \right) = \frac{x}<br />
{{1 - x}} \hfill \\

    {\text{Inverse of  }}f\left( x \right){\text{ is  }}f^{ - 1} \left( x \right) = \frac{x}<br />
{{1 - x}} \hfill \\
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  4. #4
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    Thank you! I can't believe I never saw bringing y to the left side...
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