$\"\"$

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(a)

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The function is $\"\"$ .

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Domain of logarithm function $\"\"$ is defined for all $\"\"$ or $\"\"$ .

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

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

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$\"\"$

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(b)

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Graph:

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Graph the function $\"\"$ :

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$\"\"$

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$\"\"$

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(c)

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Range of the logarithm function $\"\"$ is defined as $\"\"$ .

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Observe the graph range of $\"\"$ is $\"\"$ .

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Vertical asymptote of the logarithmic function $\"\"$ is $\"\"$ .

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Therefore, Vertical asymptote of $\"\"$ is $\"\"$ .

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The verical asymptote is $\"\"$ .

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$\"\"$

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(d)

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Find the inverse function of $\"\"$ .

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Consider $\"\"$ .

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Solve for $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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

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$\"\"$

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Therefore , $\"\"$ .

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

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$\"\"$

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(e)

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Find the domain and range of inverse function.

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The inverse function is $\"\"$ .

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

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

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

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Range of $\"\"$ is $\"\"$ .

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$\"\"$

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(f)

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Graph:

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Graph the function $\"\"$ :

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$\"\"$

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$\"\"$

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(a) The domain of $\"\"$ is $\"\"$ .

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(b) Graph of the function $\"\"$ is :

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$\"\"$

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(c) The range of $\"\"$ is $\"\"$ .

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(d) The inverse function of the $\"\"$ is $\"\"$ .

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(e) The domain of $\"\"$ is $\"\"$ .

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

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(f) Graph of the function $\"\"$ is :

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$\"\"$