Question

Identify the domain of the combined function h(x) = f(x) · g(x), if the domain of f(x) is (4, 4.5], and the domain of g(x) is [4, 4.5).The domain of h(x) is [4, 4.5] (4, 4.5) [4, 4.5) (4, 4.5]

Answer 1

the answer is b

Explanation:

Answer 2

Option 2 - (4,4.5)

Explanation:

Given : The combined function h(x) = f(x) · g(x). if the domain of f(x) is (4, 4.5], and the domain of g(x) is [4, 4.5).

To identify : The domain of h(x)?

Solution :

The given function h(x) = f(x) · g(x) is a composite function.

By definition of composite function the domain of the function is defined as the set of all values that go into the function.

The domain of f(x) is A=(4, 4.5]

The domain of g(x) is B= [4, 4.5)

h(x) = f(x) · g(x)

The domain of the function h(x) is intersection of the domain of f(x) and g(x).

`C= A\cap B`

`C= (4, 4.5]\cap [4, 4.5)`

`C= (4,4.5)`

Therefore, The domain of the function h(x) is (4,4.5).

Hence, Option 2 is correct.