If \( f: R \rightarrow R \) is a function define by \(f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi\) where [·] denot…

If \( f: R \rightarrow R \) is a function define by \(f(x)=[x-1] \cos \left(\frac{2 x-1}{2}\right) \pi\) where [·] denotes the greatest integer function, then \( f \) is:

[JEE Main 2021, 24 Feb (Shift 1)]