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AIME 2024 / AIME 2024 train 6094b21f-ab17-51f6-a1e6-622c656b3266

Problem

Answer published by the source. Consult the official source to check your work against its answer.

Problem

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=4g(f(sin(2πx))) and x=4g(f(cos(3πy))).y=4 g(f(\sin (2 \pi x))) \quad\text{ and }\quad x=4 g(f(\cos (3 \pi y))).
Plain-text mathematical notation (without MathML)
Define f(x)=||x|−(1)/(2)| and g(x)=||x|−(1)/(4)|. Find the number of intersections of the graphs of y=4g(f(sin(2πx)))  and  x=4g(f(cos(3πy))).
Original LaTeX notation
Define $f(x)=|| x|-\tfrac{1}{2}|$ and $g(x)=|| x|-\tfrac{1}{4}|$. Find the number of intersections of the graphs of \[y=4 g(f(\sin (2 \pi x))) \quad\text{ and }\quad x=4 g(f(\cos (3 \pi y))).\]

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Source and history

task_id
6094b21f-ab17-51f6-a1e6-622c656b3266
task_key
default--train--6094b21f-ab17-51f6-a1e6-622c656b3266
task_revision_id
3
config / split
default / train

Official source

initial import