$f(x) = \frac{cosx}{[\frac{2x}{\pi}] + \frac{1}{2}} $ , where x is not an integral multiple of π

Q: $ \large f(x) = \frac{cosx}{[\frac{2x}{\pi}] + \frac{1}{2}} $ , where x is not an integral multiple of π and [.] denotes the greatest integer function is

(A) an odd function

(B) even function

(C) neither odd nor even

(D) none of these

Sol: Clearly $\large [- \frac{2x}{\pi}] + \frac{1}{2} = -([ \frac{2x}{\pi}] + \frac{1}{2})$

⇒ f(x) is an odd function.

Hence (A) is the correct answer.