Problem #PRU-64770

Problems Methods Mathematical induction Mathematical induction (other) Calculus Functions of one variable. Continuity Monotonicity, boundedness Proof by contradiction

Problem

A function f is given, defined on the set of real numbers and taking real values. It is known that for any x and y such that x>y, the inequality (f(x))2f(y) is true. Prove that the set of values generated by the function is contained in the interval [0,1].