Question

For ${\sin }^{-1}\left[x\right]$, where $[.]$ is greatest integer function, which of the following is/are true?

• A. Domain is $[-1,2)$
• B. Product of all integral values of $x$ in the domain is $-1$
• C. Sum of all integral values of $x$ in the domain is $0$
• D. Domain is $\{-1,0,1\}$

Answer 1

Answer: (A), (C)

Sum of all integral values of $x$ in the domain is $0$

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 $-1,0,1$
$\therefore$ Sum $=0$
$\therefore$ Product $=0$