2021 WSMO Speed Round/Problem 1: Difference between revisions
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<cmath>=f(f(f(f(f((1-1)^2)))))=f(f(f(f(f(0)))))=f(f(f(f((0-1)^2))))=f(f(f(f(1))))=f(f(f((1-1)^2)))</cmath> | <cmath>=f(f(f(f(f((1-1)^2)))))=f(f(f(f(f(0)))))=f(f(f(f((0-1)^2))))=f(f(f(f(1))))=f(f(f((1-1)^2)))</cmath> | ||
<cmath>=f(f(f(0)))=f(f((0-1)^2))=f(f(1))=f((1-1)^2)=f(0)=(0-1)^2=\boxed{1}.</cmath> | <cmath>=f(f(f(0)))=f(f((0-1)^2))=f(f(1))=f((1-1)^2)=f(0)=(0-1)^2=\boxed{1}.</cmath> | ||
~ pinkpig | |||
Revision as of 16:34, 22 December 2021
Problem
Let 
, and let 
. Find the value of 
.
Solution (bash)
Note that
![\[|f^7(2)|=f(f(f(f(f(f(f(2)))))))=f(f(f(f(f(f((2-1)^2))))))=f(f(f(f(f(f(1))))))\]](http://latex.artofproblemsolving.com/3/3/d/33d9637d2533ffb876684aa542996fda25518c30.png)
![\[=f(f(f(f(f((1-1)^2)))))=f(f(f(f(f(0)))))=f(f(f(f((0-1)^2))))=f(f(f(f(1))))=f(f(f((1-1)^2)))\]](http://latex.artofproblemsolving.com/1/b/5/1b5fa488afbec394528cda2caed09fec8730b4ed.png)
![\[=f(f(f(0)))=f(f((0-1)^2))=f(f(1))=f((1-1)^2)=f(0)=(0-1)^2=\boxed{1}.\]](http://latex.artofproblemsolving.com/d/7/a/d7a4ba936b0fc5c7024af9f646b9b8adb31c971f.png)
~ pinkpig
