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Math Help - inverse

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    inverse

    f(t) = (2e^t + 3e^-t) / (e^t + 2e^-t) find f^-1 (t)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by helmszee View Post
    f(t) = (2e^t + 3e^-t) / (e^t + 2e^-t) find f^-1 (t)
    I will start you off.

    let y = f(t)

    we have: y = \frac {2e^t + 3e^{-t}}{e^t + 2e^{-t}}

    For inverse, switch y and t and solve for y

    \Rightarrow t = \frac {2e^y + 3e^{-y}}{e^y + 2e^{-y}}

    \Rightarrow t \left( e^y + 2e^{-y} \right) = 2e^y + 3e^{-y}

    \Rightarrow t \left( e^{2y} + 2 \right) = 2e^{2y} + 3

    \Rightarrow (t - 2)e^{2y} = 3 - 2t

    \Rightarrow e^{2y} = \frac {3 - 2t}{t - 2}

    now continue
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