Find the domain of a composition function (fog)(x) given by

Question

f
(x) = x^2 – 9 and g(x) = √(9 − x^2).

Answer 1

Step 1:

The functions are and .

The domain of is all real numbers.

The domain of :

The function under the square root should not be negative.

.

The domain of is .

Step 2:

Find .

.

The domain of is the set of all numbers in the domain of such that is in the domain of .

Domain of the composite function is .

Solution:

Domain of the composite function is .