Final answer:
The domain of the function f(x) = √(3x + 18) is the set of all x-values for which the expression inside the square root is non-negative, which gives x ≥ -6. However, considering the restriction 0 ≤ x ≤ 20, the domain of f(x) is further limited to the interval [0, 20].
Step-by-step explanation:
The question asks us to specify the domain of the function f(x) = √(3x + 18). To find the domain, we need to determine the set of all possible x-values that we can plug into the function without causing any mathematical issues, such as taking the square root of a negative number.
Since the function includes a square root, the expression inside the root must be greater than or equal to zero for the function to have real number outputs. Thus, we have 3x + 18 ≥ 0. Solving for x gives us x ≥ -6. However, based on additional information provided, we know that x is further restricted to be between 0 and 20, inclusive. Therefore, the domain of f(x) is 0 ≤ x ≤ 20.
In summary, for the function f(x) = √(3x + 18), any x-value less than -6 is outside of the function's domain due to the square root restriction. When we factor in the additional condition that 0 ≤ x ≤ 20, the domain is refined to the interval [0, 20].