2024 AIME I Problems/Problem 12: Difference between revisions
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==Problem== | |||
Define <math>f(x)=|| x|-\tfrac{1}{2}|</math> and <math>g(x)=|| x|-\tfrac{1}{4}|</math>. Find the number of intersections of the graphs of <cmath>y=4 g(f(\sin (2 \pi x))) \quad\text{ and }\quad x=4 g(f(\cos (3 \pi y))).</cmath> | |||
==Solution== | |||
==See also== | |||
{{AIME box|year=2024|n=I|num-b=11|num-a=13}} | |||
{{MAA Notice}} | |||
Revision as of 18:24, 2 February 2024
Problem
Define 
and 
. Find the number of intersections of the graphs of ![\[y=4 g(f(\sin (2 \pi x))) \quad\text{ and }\quad x=4 g(f(\cos (3 \pi y))).\]](http://latex.artofproblemsolving.com/c/c/9/cc93c9c286edc107f0d7c62bd2c31b959accc4fa.png)
Solution
See also
| 2024 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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