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Grades 11-12 Video Solutions 2013
Levels 11&12 Video Solutions 2013 problem25
Levels 11&12 Video Solutions 2013 problem25
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Video Summary
The problem involves finding the number of solutions for the function \( f^k(n) = 1 \), where \( f \) applies a rule based on whether \( n \) is even or odd. Exploring \( f^1(n) = 1 \) reveals 2 solutions: \( n = 2 \) or \( n = 3 \). Extending this, we observe that each step doubles the number of solutions, establishing a pattern. By induction, the number of solutions for \( f^{2013}(n) = 1 \) is \( 2^{2013} \). Thus, the number of solutions for the equation \( f^{2013}(n) = 1 \) is \( 2^{2013} \).
Keywords
function solutions
induction pattern
even odd rule
exponential growth
mathematical problem
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