Final answer:
The domain of the function g(x, y) = 3x - 6y is all real numbers for both x and y, because there are no limitations in the function expression that would restrict the values x and y can take.
Step-by-step explanation:
The function given, g(x, y) = 3x - 6y, is a two-variable function. The domain of a function refers to the set of all possible input values (x and y in this case) which makes the function defined.
As there are no restrictions (like denominators that should not equal zero or no square roots of negative numbers) in the function g(x, y) = 3x - 6y, the domain is all real numbers for both x and y. In notation form, this can be represented as R x R (R squared), indicating all possible pairs of real numbers (x, y).
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