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# inverse functions

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Suppose the function $f$ has all real numbers in its domain and range and is invertible. Some values of $f$ are given by the following table:$$\begin{array}{c || c | c | c | c | c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f(x) & 2 & 3 & 5 & 7 & 8 \end{array}$$What is the value of $f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5))?$ If there is not enough information to answer this question, enter "NEI".

May 3, 2021

$f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5)) = 12$.