Final answer:
The domain of the function g(x) is the set of integers from 3 to 12 inclusive, represented in set notation as {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Step-by-step explanation:
The domain of the function g(x) that models the number of tables Emma needs to set up if x guests attend her party is the set of all possible values that x, the number of guests, can take. Since the party is capped at a maximum of 12 guests and Emma knows that at least 3 guests are coming, the domain in set notation is {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. This includes all the integers between 3 and 12, inclusive, because these are the counts of guests for which the function g(x) is defined.