1997 AMC 12 Problem 27
Attempt Problem 27 of the 1997 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
Consider those functions that satisfy for all real Any such function is periodic, and there is a least common positive period for all of them. Find
Answer: D
Small hint:
For fixed , study the sequence
Big hint:
Use repeatedly to find when every initial pair returns
Solution:
For the equation is Starting from the sequence is so every such function has period This is least because satisfies the equation and has fundamental period Hence D is correct.
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