Problem #PRU-79400

Problems Algebra Functional equations Calculus Functions of one variable. Continuity Periodicity and aperiodicity
 16–16  3.0

Problem

We consider a function y=f(x) defined on the whole set of real numbers and satisfying f(x+k)×(1−f(x))=1+f(x) for some number k≠0. Prove that f(x) is a periodic function.