Final answer:
The domain and range of the function f(x) = 1/4(x√3 + 6 + √2 + 5x - 4) are both all real numbers, which means the domain is D(-∞, ∞) and the range is R(-∞, ∞).
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values). For the given function f(x) = 1/4(x√3 + 6 + √2 + 5x - 4), we can tell that the function consists of basic algebraic operations that are defined for all real numbers. There are no restrictions like division by zero or square roots of negative numbers that would limit the domain of this function. Therefore, the domain is all real numbers, which is denoted by D(-∞, ∞). As for the range, without further information on the function's transformations, we assume it is also all real numbers since it is a linear function in x when simplified. Therefore, the range is also all real numbers, denoted by R(-∞, ∞).