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The functions are $\"\"$ and $\"\"$ .

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$\"\"$ :

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All possible values of $\"\"$ is the domain of the function.

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The function under the square root should not be negative.

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So $\"\"$ .

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

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$\"\"$ :

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All possible values of $\"\"$ is the domain of the function.

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There are no constraints for a cube root function.

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The domain of $\"\"$ is the set of all real numbers.

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(a)

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Find $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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But the function under the sixth root should not be negative.

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$\"\"$

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

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(b)

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Find $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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The composite function has a cube root function, so all possible values of $\"\"$ is the domain of the function.

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

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(c)

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Find $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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But the composite function under the fourth root should not be negative.

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$\"\"$

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

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\ \

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(d)

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Find $\"\"$ .

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$\"\"$

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$\"\"$ .

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

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The composite function has a cube root function, so all possible values of $\"\"$ is the domain of the function.

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

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(a) $\"\"$ , and its domain is $\"\"$ .

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(b) $\"\"$ , and its domain is $\"\"$ .

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(c) $\"\"$ , and its domain is $\"\"$ .

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(d) $\"\"$ , and its domain is $\"\"$ .