Final answer:
The domain of the function f(x) = 2|x - 1| + 3 is all real numbers, hence the answer is option C: x.
Step-by-step explanation:
The correct answer is option C: x. The function f(x) = 2|x – 1| + 3 involves an absolute value, which can take on any real number as its input. Because there are no additional restrictions or denominators that could cause division by zero, and no square roots or logarithms that could restrict the domain, the domain of this function is all real numbers. So, for any x belonging to the real numbers, the function f(x) will have a real value.
The domain of a function refers to the set of possible input values for the function. In this case, the function f(x) = 2|x – 1| + 3 is defined for all real numbers because the absolute value function is defined for all real numbers. Therefore, the domain of f(x) is x, which means any real number can be used as input for the function.