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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R

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

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Solution

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

$∵ - 1 \leq s i n^{- 1} x \leq 1$

$∴ - 1 \leq 5 x \leq 1$

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

Hence, domain is $[- \frac{1}{5}, \frac{1}{5}]$ .

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f (x) = \frac{x}{x^{2} + 4}

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a

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