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Suppose that $f$ is a function and $f^{-1}$ is the inverse of $f$. If $f(3)=4$, $f(5)=1$, and $f(2)=5$, evaluate $f^{-1}\left(f^{-1}(5)+f^{-1}(4)\right)$.

 Jul 15, 2018
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Suppose that $f$ is a function and $f^{-1}$ is the inverse of $f$. If $f(3)=4$, $f(5)=1$, and $f(2)=5$,
evaluate $f^{-1}\left(f^{-1}(5)+f^{-1}(4)\right)$.

 

\(\begin{array}{|r|r|r|r|} \hline x & f(x) \\ \hline 2 & 5 & f(2) = 5 & f^{-1}(5) = 2 \\ 3 & 4 & f(3) = 4 & f^{-1}(4) = 3 \\ 5 & 1 & f(5) = 1 & \\ \hline f^{-1}(x) & x \\ \hline \end{array} \)

 

\(\begin{array}{|rcll|} \hline && f^{-1}\Big(f^{-1}(5)+f^{-1}(4)\Big) \\ &=& f^{-1}\left(2+3\right) \\ &=& f^{-1}(5) \\ &=& 2 \\ \hline \end{array}\)

 

 

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 Jul 16, 2018

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