Question

The domain of ${\sin }^{-1}x$ is

• A. $\left(-\mathrm{\pi },\mathrm{\pi }\right)$
• B. $\left[-1,1\right]$
• C. $\left(0,2\mathrm{\pi }\right)$
• D. $\left(-\infty ,\infty \right)$

Answer 1

The correct option is B

$\left[-1,1\right]$

Explanation for the correct option(s)

Find the domain.

Consider the given functions as,

$y={\sin }^{-1}x$

The graph of ${\sin }^{-1}x$ or $\text{arc}\sin x$ is given as

From the graph, we can write as

$$\begin{gathered} -\frac{\mathrm{\pi }}{2}\le {\sin }^{-1}x\le \frac{\mathrm{\pi }}{2} \\ -1\le {\sin }^{-1}x\le 1 \end{gathered}$$

Hence, the domain of the function is $\left[-1,1\right]$

Therefore, option B is correct.