Answer:
(B) (-∞, -1) U (-1, 2) U (2, ∞)
Explanation:
To determine the domain of the given expression, we need to identify the values for which the expression is defined. The domain represents all the possible values that the variable(s) can take.
Looking at the options provided, we can see that (A), (B), and (C) represent different intervals of values, while (D) indicates that the domain does not exist (DNE).
To determine the correct option, let's analyze the intervals provided and consider the restrictions in the expression.
(A) (-∞, -∞): This option indicates that the domain includes all real numbers. However, this is not the correct option as it is not a valid representation of an interval.
(C) (-∞, -2) U (2, ∞): This option represents an interval that includes all real numbers except for the values between -2 and 2. This means that the expression is defined for all values less than -2 and greater than 2. This is not the correct option as it does not represent the given expression.
(B) (-∞, -1) U (-1, 2) U (2, ∞): This option represents an interval that includes all real numbers except for the values between -1 and 2. This means that the expression is defined for all values less than -1 and greater than 2. This is the correct option as it accurately represents the domain of the given expression.
(D) DNE: This option indicates that the domain does not exist. However, this is not the correct answer as the domain of an expression can be defined based on the given constraints.
Therefore, the correct answer is option (B) (-∞, -1) U (-1, 2) U (2, ∞), which represents the valid intervals for the domain of the given expression.