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  1. #1
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    functions

    f(x) = 2x+1
    g(x) = 3x-5

    find g^-1 of f^-1 of 2
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DINOCALC09 View Post
    f(x) = 2x+1
    g(x) = 3x-5

    find g^-1 of f^-1 of 2
    Let $\displaystyle g(x) = y_1 = 3x - 5$

    for $\displaystyle g^{-1}$ switch $\displaystyle x$ and $\displaystyle y$ and solve for $\displaystyle y$

    so, $\displaystyle x = 3y_1 - 5$

    $\displaystyle y_1 = \frac {x + 5}3$

    thus, $\displaystyle g^{-1}(x) = \frac {x + 5}3$

    similarly, $\displaystyle f^{-1}(x) = \frac {x - 1}2$


    now can you find $\displaystyle g^{-1} \circ f^{-1}(x) = g^{-1} \left( f^{-1} (x) \right)$?
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