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

Guest Jun 22, 2020

edited by
Guest
Jun 22, 2020

edited by Guest Jun 23, 2020

edited by Guest Jun 23, 2020

edited by Guest Jun 23, 2020

edited by Guest Jun 23, 2020

#1**0 **

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**

Guest Jun 23, 2020