Question

Range of $f\left(x\right)=\left[\sin x\right]$ is given by, $[.]$ represent greatest integer function

• A. $[-1,1]$
• B. $\{-1,1\}$
• C. $\{-1,0,1\}$
• D. $[-1,-1]-\left\{0\right\}$

Answer 1

Answer: (C)

$\{-1,0,1\}$

We know, $\sin \left(x\right)\in [-1,1]$

Now, $[-1]=-1$ ,$\left[0\right]=0$ and $\left[1\right]=1$.

Now for, $\sin \left(x\right)\in (-1,0)$

We get
$\left[\sin \right(x\left)\right]=-1$

for
$\sin \left(x\right)\in (0,1)$

We get,
$\left[\sin \right(x\left)\right]=0$

Hence, $f\left(x\right)=\left[\sin \right(x\left)\right]$.

Range, $\in \{-1,0,1\}$.