The function `f(x)=((1)/(2))^(sinx)`, is

Options

A. periodic with period `2pi`
B. an odd function
C. not expressible as the sum of an even function and an odd function
D. none of these

Answer

To analyze the function \( f(x) = \left(\frac{1}{2}\right)^{\sin x} \), we will go through the properties of periodicity, oddness, and evenness step by step.

### Step 1: Check if the function is periodic
The function \( f(x) = \left(\frac{1}{2}\right)^{\sin x} \) depends on \( \sin x \). We know that \( \sin x \) is a periodic function with a period of \( 2\pi \). Therefore, \( f(x) \) will also inherit this periodicity.

**Conclusion:** The period of \( f(x) \) is \( 2\pi \).