Answer:
Option 2 - (4,4.5)
Step-by-step 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).
[tex]C= A\cap B[/tex]
[tex]C= (4, 4.5]\cap [4, 4.5)[/tex]
[tex]C= (4,4.5)[/tex]
Therefore, The domain of the function h(x) is (4,4.5).
Hence, Option 2 is correct.
