State the domain of the composite function

Question

f(x) = x^2 g(x) = x^2 +4

a) fog   b) gof   c) fof  d) gog

Answer 1

Step 1:

The functions are and .

The domain of is set of all real numbers.

The domain of is set of all real numbers.

(a)

Find .

                        ( Since )

The domain of the inside function is .

The composite function has no restrictions, so all possible values of is domain of the function.

The domain of is .

Step 2:

(b)

Find .

The domain of the inside function is .

The composite function has no restrictions, so all possible values of is domain of the function.

The domain of is .

Solutions :

(a) and its domain is .

(b) and its domain is .

Answer 2

Step 1:

The functions are and .

The domain of is set of all real numbers.

The domain of is set of all real numbers.

(c)

Find .

The domain of the inside function is .

The composite function has no restrictions, so all possible values of is domain of the function.

The domain of is .

Step 2:

(d)

Find .

The domain of the inside function is .

The composite function has no restrictions, so all possible values of is domain of the function.

The domain of is .

Solutions :

(c) and its domain is .

(d) and its domain is .