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 domain of h must be in both f and g

Answer 2

hint... look at the end points

Answer 3

So the domain is basically the range of x values that can be plugged into a function, correct?
If you can plug a value into f but you can't plug it into g, then it can't be in the domain of h.
The ( and ] type brackets mean different things (exclusive, inclusive) for the end values. Does this make sense?

Answer 4

In PM you asked me if the answer was [4, 4.5]. I think you might have it flipped. the [ means including the very last value, and ( means not. In other words, [ is a filled in circle on a number line, and ( is an empty/hollow circle.
If f(x) contains 4.5 but does not contain 4 because of the ( , and g(x) contains 4 but does not contain 4.5 because of the ), then h(x) cannot have 4 or 4.5 in its domain, because 4 cannot be plugged into both f(x) and g(x) (which make up h(x),) and the same goes for 4.5

So the correct answer would actually be (4, 4.5), because, why?