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Inverse Function

The domain of...

Question

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

A

[- \frac{π}{5}, \frac{π}{5}]

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B

[- \frac{π}{10}, \frac{π}{10}]

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C

R

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D

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

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Solution

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

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Inverse Function

Standard XII Mathematics

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