Final answer:
To make the inverse of a constant function f(x) = (-1)² a function, the domain of f(x) must be restricted to a single value. A common choice for the restriction is just {0}, making the function a one-to-one correspondence between input and output.
Step-by-step explanation:
The question deals with the concept of functions and their inverses in algebra. Specifically, it asks what restriction on the domain of a constant function, represented as f(x) = (-1)², would make its inverse, denoted as f−1(x), also a function. Since f(x) is a constant function, we know it always outputs the same result regardless of x, which is 1 in this case because (-1)² = 1. A function's inverse exists if the original function is one-to-one, meaning each output is associated with exactly one input.
To ensure f(x) is one-to-one, and hence its inverse exists as a function, we must restrict the domain of f(x) to any single value. A common choice is to restrict x to x=0 only. Thus, the domain of f(x) would be just {0}, and the range would still be {1}. With this restriction, the inverse function f−1(x) would map 1 back to 0, making it a valid function as well.