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Silly Extra Intersection

Source: 2024 AIME I Problem 12

February 2, 2024
AIMEAIME I

Problem Statement

Define f(x)=∣∣x∣−12∣f(x)=|| x|-\tfrac{1}{2}| and g(x)=∣∣x∣−14∣g(x)=|| x|-\tfrac{1}{4}|. Find the number of intersections of the graphs of y=4 g(f(\sin (2 \pi x)))  \text{ and }  x=4 g(f(\cos (3 \pi y))).
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