Problem #PRU-65842

Problems Methods Examples and counterexamples. Constructive proofs Algebra Functional equations Calculus Functions of one variable. Continuity Functions. Continuity (other)

Problem

Are there functions \(p (x)\) and \(q (x)\) such that \(p (x)\) is an even function and \(p (q (x))\) is an odd function (different from identically zero)?