Final answer:
The domain of the function is [0, ∞) and the range of the function is [0, ∞).
Step-by-step explanation:
The given function is f(x) = -√(3x).
The domain of a function is the set of all possible input values, or x-values, for which the function is defined. In this case, since we are taking the square root of 3x, the inside of the square root must be greater than or equal to 0. So we need to solve the inequality 3x ≥ 0. Dividing both sides by 3, we find x ≥ 0. Therefore, the domain of the function is all values of x greater than or equal to 0, or [0, ∞).
The range of a function is the set of all possible output values, or y-values, for which the function takes on. For this function, taking the square root of a non-negative number will always result in a non-negative number. Therefore, the range of the function is all values of y greater than or equal to 0, or [0, ∞).
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