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 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

 Jun 22, 2020
edited by Guest  Jun 22, 2020
edited by Guest  Jun 23, 2020
edited by Guest  Jun 23, 2020
 #1
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+1

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

 Jun 23, 2020
 #2
avatar+21953 
0

I can't interpret the question.

 Jun 23, 2020
 #3
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0

Just use a latex calculator

Guest Jun 23, 2020
 #4
avatar+1710 
0

I'll give hints if you make it readable...

 Jun 23, 2020
 #5
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0

ok 

f(n) includes n^2+1 is odd and n/2 is even. For how many integers n from 1 to 100 does f(f(...f(n)...)) =1 for some number of applications of f?

 

can u please use a latex calculator for the other one?

Guest Jun 23, 2020

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