Problem #PRU-79595

Problems Algebra Algebra Functional equations

Problem

The function \(f (x)\) for each real value of \(x\in (-\infty, + \infty)\) satisfies the equality \(f (x) + (x + 1/2) \times f (1 - x) = 1\).

a) Find \(f (0)\) and \(f (1)\). b) Find all such functions \(f (x)\).