Final answer:
The domain of the function v(x) = sqrt(2x + 16) is x ≥ -8.
Step-by-step explanation:
The domain of a function represents the set of all possible input values for the function. In this case, the function is v(x) = sqrt(2x + 16). To find the domain, we need to consider the values that can be plugged into the function without resulting in any undefined or imaginary outputs.
The function v(x) involves taking the square root of a quantity (2x + 16). In order for the square root to be defined, the quantity inside the square root must be greater than or equal to zero. In other words, 2x + 16 ≥ 0.
To solve the inequality 2x + 16 ≥ 0, we subtract 16 from both sides to get 2x ≥ -16. Then, by dividing both sides by 2, we find x ≥ -8. Therefore, the domain of the function v(x) = sqrt(2x + 16) is x ≥ -8.