The functions are and .

Find .

The sum is the function defined by : .

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Domain of = domain of  domain of .

All possible values of is domain of a function.

Numerator of the rational function is a radical expression.

So the expression under the square root (the radicand) must be nonnegative .

Find which number make the fraction undefined, create an equation where the denominator is not equal to zero.

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The domain of is all real numbers and does not equals to 0.

Thus, the domain of is .

Find .

The difference is the function defined by : .

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Domain of = domain of  domain of .

All possible values of is domain of a function.

Numerator of the rational function is a radical expression.

So the expression under the square root (the radicand) must be nonnegative .

Find which number make the fraction undefined, create an equation where the denominator is not equal to zero.

.

The domain of is all real numbers and does not equals to 0.

Thus, the domain of is .

Find .

The product is the function defined by : .

.

Domain of = domain of  domain of .

All possible values of is domain of a function.

Numerator of the rational function is a radical expression.

So the expression under the square root (the radicand) must be nonnegative .

Find which number make the fraction undefined, create an equation where the denominator is not equal to zero.

.

The domain of is all real numbers and does not equals to 0.

Thus, the domain of is .

Find .

The quotient is the function defined by : .

.

Domain of = domain of  domain of .

All possible values of is domain of a function.

Numerator of the rational function is a radical expression.

So the expression under the square root (the radicand) must be nonnegative .

Thus, the domain of is .

Find .

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Substitute in .

.

Find .

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Substitute in .

.

Find .

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Substitute in .

.

Find .

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Substitute in .

.

, domain is .

, domain is .

, domain is .

, domain is .

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.

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