It is known that the function f (x) whose domain is r satisfies that f (f (x) - x2 + x) = f (x) - x2 + X has only one real number x0, such that f (x0) = x0 Why should the two values obtained from the analytic expression of function f (x) be rounded off x = 0?

It is known that the function f (x) whose domain is r satisfies that f (f (x) - x2 + x) = f (x) - x2 + X has only one real number x0, such that f (x0) = x0 Why should the two values obtained from the analytic expression of function f (x) be rounded off x = 0?

According to the meaning f (f (x) - x ^ 2 + x) = f (x) - x ^ 2 + X and f (x0) = x0: F (x0) - x0 ^ 2 + x0 = x0 substitute f (x0) = x0 into: x0-x0 ^ 2 + x0 = X0 solve this equation: x0 = 0 or x0 = 1 verify: if x0 = 0, then the function always satisfies f (x) - x ^ 2 + x = 0, so the analytic expression of the function is f (x) = x ^ 2-x