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Math Help - inverse functions

  1. #1
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    Unhappy inverse functions

    how do you find the inverse of f(X)=2^ -x ?

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  2. #2
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    Hello, ericchung912!

    How do you find the inverse of: . f(x)\:=\:2^{-x} ?

    We have: . f(x) \;=\;2^{-x}

    Replace y with f(x)\!:\;\;y \;=\;2^{-x}

    Switch x's and y's: . x \;=\;2^{-y}


    Solve for y: . 2^{-y} \;=\;x

    Take logs: . \ln\left(2^{-y}\right) \;=\;\ln(x) \quad\Rightarrow\quad -y\!\cdot\!\ln(2) \;=\;\ln(x) \quad\Rightarrow\quad y \;=\;-\frac{\ln(x)}{\ln(2)}

    Therefore: . f^{-1}(x) \;=\;-\frac{\ln(x)}{\ln(2)}

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