f(x)=( x)/([(2 x)/(π)]+(1)/(2)) , where x is not an integral...

f(x)=\frac{\cos x}{\left[\frac{2 x}{\pi}\right]+\frac{1}{2}}

, where x is not an integral multiple of

\pi

and [.] denotes the greatest integer function, is f(x)=( x)/([(2 x)/(π)]+(1)/(2)) , where x is not an integral multiple of π and [.] denotes the greatest integer

Options

Aan odd function
Ban even function
Cneither odd nor even
DNone of these

Correct answer

A. an odd function

Step-by-step solution

=-\frac{\cos x}{\left[\frac{2 x}{\pi}\right]+\frac{1}{2}}=-f(x)

Therefore,

f(x)

is an odd function.

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