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

 May 3, 2021

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