$\"\"$

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The function is $\"\"$ .

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The function is continuous in the interval $\"\"$ .

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Derivative of $\"\"$ is $\"\"$ , which is positive in the interval $\"\"$ .

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So the function is one to one and is strictly monotonic.

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Find the inverse of the function.

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If $\"\"$ , then $\"\"$ .

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$\"\"$ \ \

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To find the inverse of a function interchange the variables $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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Inverse function is $\"\"$ .

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$\"\"$

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The inverse function is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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The function $\"\"$ is monotonic and has an inverse $\"\"$ .

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$\"\"$ .