Final answer:
The inverse of f(x) = x^2 is not a function because f(x) = x^2 is not one-to-one, resulting in the same output for two different inputs. However, by restricting the domain, the inverse can become a function.
Step-by-step explanation:
The question asks if the inverse of the function f(x) = x^2 is also a function. The answer is False because the function f(x) = x^2 is not one-to-one. A function is one-to-one if each output is the result of exactly one input. For f(x) = x^2, both input values x = a and x = -a produce the same output a^2. Therefore, the inverse of f(x) = x^2 would not pass the vertical line test and is not a function. However, if we restrict the domain of f(x) to non-negative numbers (x ≥ 0 or x ≤ 0), the inverse would then be a function, represented by f-1(x) = ±√x, since each output would then come from a unique input.