`f(x)=(cosx)/([(2x)/pi]+1/2),` where `x` is not an integral multiple of `pi` and `[dot]` denotes the greatest integer function, is an odd function an even function neither odd nor even none of these

Options

A. an odd function
B. an even function
C. neither odd nor even
D. None of these

Answer

A

Explanation

`f(-x)=(cos(-x))/([-(2x)/(pi)]+(1)/(2))=(cosx)/(-1-[(2x)/(pi)]+(1)/(2))`(As x is not an integral multiple of `pi`)
`= -(cosx)/([(2x)/(pi)]+(1)/(2))= -f(x)`
Therefore, `f(x)` is an odd function.