Question

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

Answer 1

Correct Answer - A
`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.