Question

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

• A. $[-\frac{1}{3},\frac{1}{3}]$
• B. $(-\frac{1}{3},\frac{1}{3})$
• C. $(0,\frac{1}{3})$
• D. $(-\frac{1}{3},0)$

Answer 1

The correct option is A $[-\frac{1}{3},\frac{1}{3}]$

${\sin }^{-1}y$ is defined for $y\in [-1,1]$

$\therefore {\sin }^{-1}3x$ is defined for $3x\in [-1,1]$

$\Rightarrow -1\le 3x\le 1$

$\Rightarrow \frac{-1}{3}\le x\le \frac{1}{3}$

$x\in [\frac{-1}{3},\frac{1}{3}]$