Question

The function $f\left(x\right)={\left(\frac{1}{2}\right)}^{\sin x}$ is

• A. periodic with period $2\pi$
• B. an odd function
• C. expressible as the sum of an even function and an odd function
• D. none of these

Answer 1

Answer: (A), (C)

The correct options are
A periodic with period $2\pi$
C expressible as the sum of an even function and an odd function

Given function is periodic with period $2\pi$ since period of $\sin x$ is $2\pi$

Also every function can be written as sum of and odd and an even function.

Hence option 'A' and 'C' are correct choices.