f:R→[−1,∞) and f(x)=ln⁡([|sin⁡2x|+|cos⁡2x|]) (where [.] is the greatest integer function.) Then,

The period of f(x)=|sin⁡2x|+|cos⁡2x| is π/4.So, [f(x)] is also periodic with period π/4.Also, 1≤f(x)≤2Thus, [f(x)]=1,f(x) is a many-one and into function.