Problem #PRU-109509

Problems Calculus Functions of one variable. Continuity Certain properties of a function and recurrence relations. Real numbers Rational and irrational numbers

Problem

Find all functions \(f (x)\) defined for all positive \(x\), taking positive values and satisfying the equality \(f (x^y) = f (x)^f (y)\) for any positive \(x\) and \(y\).