The functions are  and .

(a )

Find .

The sum is the function defined by : .

All possible values of  is the domain of a function.

Since is a quadratic function, the domain is all real numbers.

The domain of is set of all real numbers.

(b )

Find .

The difference is the function defined by : .

.

All possible values of  is the domain of a function.

Since is a quadratic function, the domain is all real numbers.

The domain of is set of all real numbers.

(c )

Find .

The product is the function defined by : .

All possible values of  is the domain of a function.

Since is a polynomial function, the domain is all real numbers.

The domain of is set of all real numbers.

(d )

Find .

The quotient is the function defined by : .

All possible values of  is domain of a function.

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 except .

(e )

Find .

.

Substitute in .

.

(f )

Find .

.

Substitute in .

.

(g )

Find .

.

Substitute in .

.

(h )

Find .

.

Substitute in .

.

(a ) and the domain is all real numbers.

(b ) and the domain is all real numbers.

(c ) and the domain is all real numbers.

(d ) and the domain is all real numbers except .

(e ) .

(f ) .

(g ) .

(h ) .