$\"\"$

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(a)

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The function is $\"\"$ .

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The domain of a function is all values of $\"\"$ , those makes the function mathematically correct.

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The domain of the logarithm function is always greater than zero.

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$\"\"$ and $\"\"$

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$\"\"$

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$\"\"$

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Therefore,the domain of the function is $\"\"$ .

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$\"\"$

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(b)

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The function is $\"\"$ .

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Consider $\"\"$ , then $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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

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$\"\"$

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Therefore , $\"\"$

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The inverse function is $\"\"$ .

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$\"\"$

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The inverse function is $\"\"$ .

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The domain of a function is all values of $\"\"$ , those makes the function mathematically correct.

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The domain of the exponential function is all real numbers.

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The domain of the inverse function is $\"\"$ .

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$\"\"$

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(a) The domain of the function is $\"\"$

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(b) The inverse function is $\"\"$ .

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The domain of the inverse function is $\"\"$ .