Difference between revisions of "2021 WSMO Speed Round/Problem 1"

(Created page with "==Problem== Let <math>f^1(x)=(x-1)^2</math>, and let <math>f^n(x)=f^1(f^{n-1}(x))</math>. Find the value of <math>|f^7(2)|</math>. ==Solution (bash)== Note that \begin{align...")
 
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==Problem==
 
Let <math>f^1(x)=(x-1)^2</math>, and let <math>f^n(x)=f^1(f^{n-1}(x))</math>. Find the value of <math>|f^7(2)|</math>.
 
  
==Solution (bash)==
 
Note that
 
\begin{align*}
 
|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))))))\
 
&=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)))\
 
&=f(f(f(0)))\
 
&=f(f((0-1)^2))\
 
&=f(f(1))\
 
&=f((1-1)^2)\
 
&=f(0)\
 
&=(0-1)^2=\boxed{1}
 
\end{align*}
 

Latest revision as of 16:47, 22 December 2021