Question

Find the period, if $f\left(x\right)=\sin x+\left\{x\right\}$, where $\left\{x\right\}$ is fractional part of $x$

• A. $1$
• B. $2\pi$
• C. $\pi$
• D. $f\left(x\right)$ is not periodic

Answer 1

Answer: (D)

$f\left(x\right)$ is not periodic

Here, $\sin x$ is periodic with period $2\pi$, and $\left\{x\right\}$ is periodic with period $1$.
LCM of $2\pi$ and $1$ does not exist
Thus, $f\left(x\right)$ is not periodic.