Question

If $f\left(x\right)=\sin \sqrt{x}$, then period of $f\left(x\right)$ is

• A. $\mathrm{\pi }$
• B. $\frac{\mathrm{\pi }}{2}$
• C. $2\mathrm{\pi }$
• D. None of these.

Answer 1

The correct option is D

None of these.

Explanation for the correct option.

Find the period of $f\left(x\right)$:

Given,

$f\left(x\right)=\sin \sqrt{x}$.

Concept: If $f\left(x\right)=\sin x$, then the period is $2\mathrm{\pi }$.

$\begin{array}{rcl}\sqrt{x}& =& 0,2\mathrm{\pi },4\mathrm{\pi },...\\ & \Rightarrow & \mathrm{x}=0,4{\mathrm{\pi }}^2,16{\mathrm{\pi }}^2,...\end{array}$

Since, the difference between two consecutive term is not constant,

Therefore, $f\left(x\right)$ is not periodic.

Hence, the correct option is D.