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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==Solution (bash)== | ==Solution (bash)== | ||
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− | + | <cmath>|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))))))</cmath> | |
− | |f^7(2)| | + | <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> | |
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Revision as of 16:33, 22 December 2021
Problem
Let , and let . Find the value of .
Solution (bash)
Note that