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

Problem

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Problem

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))).

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: 2
config / split: default / train

Official source

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