write the domain and range of đť‘“^-1 (đť‘Ą) = (x-3)^2
Domain: For any function, the domain is the set of all possible input values. In this case, the original function is f(x) = (x-3)^2, so the domain of f^-1(x) = (x-3)^2 is the same as the range of f(x). In the function f(x) = (x-3)^2, there are no restrictions on the input values of x, so the domain is all real numbers.
Range: For any function, the range is the set of all possible output values. The range of f^-1(x) = (x-3)^2 can be determined by looking at the output values of the original function f(x) = (x-3)^2. The function (x-3)^2 is a square of a real number, so it can never be negative. Therefore, the range of f(x) is all non-negative real numbers. This implies that the range of f^-1(x) = (x-3)^2 is all non-negative real numbers.