Question

Period of $f\left(x\right)=\log \left({\sin }^{-1}(x-\left[x\right])\right)$ is ( where $\left[x\right]$ denotes the greatest integer function) $1$

• A. $2\pi$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $1$

Answer 1

The correct option is D $1$

$f\left(x\right)=\log {\sin }^{-1}\left(x-\left[x\right]\right)\left[x-\left[x\right]=\left\{x\right\}\right]$

and period of fractional function is (1)

Hence, period of $f\left(x\right)is1$