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 \((f (x)) ^2 \leq f (y)\) is true. Prove that the set of values generated by the function is contained in the interval \([0,1]\).