Question

Find the function (a) f o g, (b) g o f , (c) f o f, and (d) g o g and their domain.

f(x) = x - 2,   g(x) = x² + 3x + 4

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 .

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 .