Question

The domain of the function $f\left(x\right)={\sin }^{-1}\left(5x\right)$ is

• A. $[-\frac{\pi }{5},\frac{\pi }{5}]$
• B. $[-\frac{\pi }{10},\frac{\pi }{10}]$
• C. $R$
• D. $[-\frac{1}{5},\frac{1}{5}]$

Answer 1

The correct option is D $[-\frac{1}{5},\frac{1}{5}]$

Given,
$f\left(x\right)={\sin }^{-1}\left(5x\right)$
$\because -1\le 5x\le 1$
$\therefore -\frac{1}{5}\le x\le \frac{1}{5}$
Hence, domain is $[-\frac{1}{5},\frac{1}{5}]$