$\"\"$

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The function is $\"\"$ , for $\"\"$ .

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Rewrite the function as $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ for all $\"\"$ , then $\"\"$ has an inverse.

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$\"\"$

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Find the inverse function.

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$\"\"$ .

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

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$\"\"$

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Solve for $\"\"$ .

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$\"\"$

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$\"\"$

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Take natural logarithm on each side.

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$\"\"$

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Apply power rule of logarithm : $\"\"$ .

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$\"\"$

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$\"\"$

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Replace $\"\"$ with $\"\"$ .

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$\"\"$ .

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Therefore, the inverse function is $\"\"$ .

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The inverse function exists only for $\"\"$ .

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$\"\"$

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The inverse function is $\"\"$ .

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The inverse function exists only for $\"\"$ .