Question

The domain of the function $y={\sin }^{-1}\left(-x^2\right)$ is

• A. $[0,1]$
• B. $1,0]$
• C. $[-1,1]$
• D. $\varphi$

Answer 1

Answer: (C)

Given, $y={\sin }^{-1}\left(-x^2\right)$
$\Rightarrow \sin y=-x^2$
We know that, $-1\le \sin y\le 1$
$\Rightarrow -1\le -x^2\le 1\Rightarrow -1\le x^2\le 1$
$\Rightarrow 0\le x^2\le 1\Rightarrow |x\mid \le 1$
$\Rightarrow -1\le x\le 1$