Question 1:
The values of a function $f(x)$ are given in the table below.\begin{tabular}{|r||c|c|c|c|c|c|} \hline $x$ & 1 & 2 & 3 & 5 & 8 & 13 \\ \hline $f(x)$ & 3 & 13 & 8 & 1 & 0 & 5 \\ \hline \end{tabular}If $f^{-1}$ exists, what is $f^{-1}\left(\frac{f^{-1}(5) +f^{-1}(13)}{f^{-1}(1)}\right)$?
Question 2:
Let
$
f(n) =
\begin{cases}
n^2+1 & \text{if }n\text{ is odd} \\
\dfrac{n}{2} & \text{if }n\text{ is even}
\end{cases}.
$
For how many integers n from 1 to 100, inclusive, does $f ( f (\dotsb f (n) \dotsb )) = 1$ for some number of applications of f?https://artofproblemsolving.com/class/2411-algebra-b/alcumus
I also take in the explanation and process it, this is an AoPS problem if you are wondering, but this topic is very confusing to me. I would greatly apreciate it if I get an answer in the next 30 minutes, and if not I would re try the problem until I get it. AGAIN I AM NOT CHEATING OFF THE ANSWERS
