Question 12
Define $f(x) = \left||x| - \tfrac{1}{2}\right|$ and $g(x) = \left||x| - \tfrac{1}{4}\right|.$ Find the number of intersections of the graphs of $$
y = 4g(f(\sin(2\pi x)))
$$ and $$
x = 4g(f(\cos(3\pi y))).
$$
y = 4g(f(\sin(2\pi x)))
$$ and $$
x = 4g(f(\cos(3\pi y))).
$$