Answer: In my opinion, The correct answer is option a: (-∞, 0) (0, ∞).
The domain of a rational function is the set of all possible input values, or x-values, for which the function is defined. In this case, the given rational function does not have any restrictions on the denominator, which is a polynomial.
Let's analyze the options one by one:
a) (-∞, 0) (0, ∞): This option represents all real numbers except 0. Since the given rational function does not have any restrictions on the denominator, it is defined for all real umbers except 0. Therefore, this is the correct answer.
b) (-∞, 1) (1, ∞): This option represents all real numbers except 1. However, there is no specific information in the question that indicates any restriction on the function when x = 1. Hence, this option is not correct.
c) (-∞, 5) (5, ∞): This option represents all real numbers except 5. Similar to option b, there is no specific information in the question that indicates any restriction on the function when x = 5. Therefore, this option is not correct.
d) (-∞, -5) (-5, ∞): This option represents all real numbers except -5. Again, there is no specific information in the question that indicates any restriction on the function when x = -5. Hence, this option is not correct.
In summary, the correct domain for the given rational function is option a: (-∞, 0) (0, ∞), which includes all real numbers except 0.