Sure, let's understand the domain restrictions for each listed function.
A) The function f(x) = x^3 is defined for all real numbers. This is because you can cube any real number and get a valid result. Therefore, the domain is all real numbers, which means it's unrestricted.
B) The function f(x) = 3 - 2x is similarly defined for all real numbers. Regardless of the value of x, you'll always get a valid result by substituting it in this function. That means the domain of this function is also unrestricted, encompassing all real numbers.
C) The function f(x) = 1/x behaves differently. While this function is defined for most real numbers, it's not defined when x = 0. This is because division by zero is undefined in mathematics. Therefore, the domain of this function is all real numbers except for zero. This constitutes a restriction in the domain.
D) Lastly, the function f(x) = x^2, like the first two functions, is defined for all real numbers. Squaring any real number gives you a real result, meaning the domain for this function is unrestricted.
After analyzing each function, we can see that the function with a restricted domain is C) f(x) = 1/x, as it is not defined when x = 0.