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
O [4, 4.5]
O (4,4.5)
O [4,4.5)
O (4,4.5)

Answer 1

The domain of h(x) is [4,4.5).

Since f(x) has a domain of (4, 4.5) and g(x) has a domain of [4, 4.5), the domain of h(x) is the intersection of the domains of f(x) and g(x), which is [4, 4.5).

Note that the left endpoint 4 is included in the domain because it is included in the domain of g(x), even though it is not included in the domain of f(x).