$\"\"$

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The function is $\"\"$ .

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Find the inverse function.

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Change $\"\"$ to $\"\"$ .

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$\"\"$ .

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Interchange $\"\"$ and $\"\"$ .

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$\"\"$ .

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Divide each side by 3.

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$\"\"$

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Apply inverse trigonometric property: $\"\"$ .

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$\"\"$

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$\"\"$

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The inverse function is $\"\"$ . $\"\"$

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Find the range of $\"\"$ :

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$\"\"$ .

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Divide each side by $\"\"$ .

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$\"\"$

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Range of the sine function: $\"\"$ .

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Here $\"\"$ .

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$\"\"$

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$\"\"$

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The range of $\"\"$ is $\"\"$ or $\"\"$ . $\"\"$

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The Domain of of $\"\"$ is range of $\"\"$ .

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The range of $\"\"$ is $\"\"$ .

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Hence the domain of $\"\"$ is $\"\"$ .

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The Range of of $\"\"$ is same as domain of $\"\"$ .

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The domain of $\"\"$ is $\"\"$ .

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Hence the range of of $\"\"$ is $\"\"$ . $\"\"$

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The inverse function is $\"\"$ .

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The range of $\"\"$ is $\"\"$ .

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The domain of $\"\"$ is $\"\"$ .

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The range of of $\"\"$ is $\"\"$ .