Step 1:

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The vector function is $\"\"$ .

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$\"\"$

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Component functions of $\"\"$ are

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$\"\"$

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$\"\"$

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$\"\"$ .

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Step 2:

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Domain of $\"\"$ consists of all values of $\"\"$ .

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Domain of $\"\"$ .

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$\"\"$ is square root function.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Domain of $\"\"$ .

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$\"\"$ is a exponential function and its domain is all real numbers.

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Domain of $\"\"$ .

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$\"\"$ is a logarithmic function and the domian of logarithmic function is real numbers greater than zero.

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log of a negative value undefined.

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$\"\"$

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$\"\"$

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Domain of $\"\"$ is $\"\"$ .

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Step 3:

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Domain of vector function is intersection of three component functions.

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$\"\"$

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$\"\"$

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Domain of $\"\"$ is $\"\"$ .

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Solution:

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Domain of $\"\"$ is $\"\"$ .

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