Question

The function \[ f(x) = \frac{\cos x}{\left\lfloor \frac{2x}{\pi} \right\rfloor + \frac{1}{2}}, \] where \( x \) is not an integral multiple of \( \pi \) and \( \lfloor \cdot \rfloor \) denotes the greatest integer function, is:

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

Hint:

A function is odd if \( f(-x) = -f(x) \) and even if \( f(-x) = f(x) \).