<p>Define <img alt="$f(x)=|| x|-\tfrac{1}{2}|$" height="23" src="https://latex.artofproblemsolving.com/2/2/b/22bcc39a38a900e76101b8a90f95f9236b2d9abf.png" width="125" /> and <img alt="$g(x)=|| x|-\tfrac{1}{4}|$" height="23" src="https://latex.artofproblemsolving.com/5/5/2/55286339b7f4fe2b23ad1ea5478be680e1893492.png" width="123" />. Find the number of intersections of the graphs of<img alt="\[y=4 g(f(\sin (2 \pi x))) \quad\text{ and }\quad x=4 g(f(\cos (3 \pi y))).\]" height="18" src="https://latex.artofproblemsolving.com/c/c/9/cc93c9c286edc107f0d7c62bd2c31b959accc4fa.png" width="392" /></p>

Question No: 426

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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Tags: Algebra

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