Question

The domain of ${\sin }^{-1}\left(3x\right)$ is

• A. $\left(-1,1\right]$
• B. $\left(-3,3\right]$
• C. $\left(-3,3\right)$
• D. $\left(\frac{-1}{3},\frac{1}{3}\right]$
  

Answer 1

The correct option is D $\left(\frac{-1}{3},\frac{1}{3}\right]$


$\mathrm{Let}{\sin }^{-1}3x=\theta$
$\Rightarrow 3x=\sin \theta$
$\mathrm{Now},-1\le \sin \theta \le 1$
$\Rightarrow -1\le 3x\le 1$
$\therefore -\frac{1}{3}\le x\le \frac{1}{3}$