Question

If $a,b$ and $c$ are the integers that satisfy the domain of ${\sin }^{-1}\left[x\right]$, where $[.]$ is the greatest integer function, then

• A. $a+b+c=0$
• B. $|a+b+c|=1$
• C. $abc=0$
• D. $|abc|=1$

Answer 1

Answer: (A), (C)

$abc=0$

Domain of ${\sin }^{-1}\left(x\right)$ is $[-1,1]$
$\Rightarrow -1\le \left[x\right]\le 1$
$\Rightarrow x\in [-1,2)$
Integers in the above interval are $-1,0,1$
$\therefore a,b,c\in \{-1,0,1\}$