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

(- \frac{1}{5}, \frac{1}{5})

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[- \frac{1}{5}, \frac{1}{5}]

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(0, \frac{1}{5})

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Solution

The correct option is D $[- \frac{1}{5}, \frac{1}{5}]$
Given $f (x) = {sin}^{- 1} 5 x$

Domain of ${sin}^{- 1} a$ is $[- 1, 1]$
Hence,
$- 1 \leq a \leq 1$
$- 1 \leq 5 x \leq 1$

$\frac{- 1}{5} \leq x \leq \frac{1}{5}$

$∴$ the domain of the function $f (x) = {sin}^{- 1} 5 x$ is $[\frac{- 1}{5}, \frac{1}{5}]$

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