Final answer:
The domain of the function is all real numbers except for x = 3 and x = -3.
Step-by-step explanation:
The domain of a function is set of all possible input values (x-values) for which function is defined. In this case, we have a rational function, so we need to ensure that the denominator is not equal to zero. To find the domain of the function g(x) = 2x/((x^2)-9)
Step 1: Set the denominator (x^2 - 9) equal to zero and solve for x.
(x^2 - 9) = 0
(x - 3)(x + 3) = 0
x = 3 or x = -3
Step 2: The domain of the function is all real numbers except for x = 3 and x = -3. Therefore, the domain of the function g(x) = 2x/((x^2)-9) is (-∞, -3) ∪ (-3, 3) ∪ (3, ∞).
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