Find a function whose graph intersects the graph in 3 places

Question

Find a function whose graph intersects the graph of f(x)= cos(x) in exactly three places.

Answer 1

Since cos(0)=cos(2pi)=cos(4pi)=1 let g(x)=1 when 0≤x≤4pi, and g(x)=2 otherwise. Then g is your function.