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Thread: 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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    $\displaystyle y = \frac{x}{x+1}$

    Swap x and y and slove for y

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

    $\displaystyle x(y+1) =y$

    $\displaystyle xy +x -y = 0$

    $\displaystyle xy -y = -x$

    $\displaystyle y(x-1) = -x$

    $\displaystyle f^{-1}(x)=\frac{-x}{x-1}$
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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.
    $\displaystyle f\left( x \right) = \frac{x}
    {{x + 1}} \hfill \\$

    $\displaystyle {\text{Let, }}y = \frac{x}
    {{x + 1}} \hfill \\$

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

    $\displaystyle \Rightarrow x = \frac{y}
    {{y + 1}} \hfill \\$

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

    $\displaystyle \Rightarrow xy + x = y \hfill \\$

    $\displaystyle \Rightarrow x = y - xy \hfill \\$

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

    $\displaystyle \Rightarrow y = \frac{x}
    {{1 - x}} \hfill \\$

    $\displaystyle \Rightarrow f^{ - 1} \left( x \right) = \frac{x}
    {{1 - x}} \hfill \\$

    $\displaystyle {\text{Inverse of }}f\left( x \right){\text{ is }}f^{ - 1} \left( x \right) = \frac{x}
    {{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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