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

Options

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

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.