On global periodicity of a class of difference equations

We show that the difference equation x(n) = f(3)( x(n-1)) f(2)(x(n-2)) f(1)( x(n-3)), n is an element of N-0, where f(i) is an element of C[(0, infinity), (0, infinity)], i is an element of {1, 2,3}, is periodic with period 4 if and only if f(i)( x) = c(i)/ x for some positive constants c(i), i is an element of {1, 2,3} or if f(i)( x) = c(i)/ x when i = 2 and f(i)( x) = c(i)x if i is an element of {1,3}, with c(1)c(2)c(3) = 1. Also, we prove that the difference equation x(n) = f(4)( x(n-1)) f3( x(n-2)) f(2)( x(n-3)) f(1)( x(n-4)), n is an element of N-0, where f(i) is an element of C[(0, infinity), (0, infinity)], i is an element of {1, 2, 3,4}, is periodic with period 5 if and only if f(i)( x) = c(i)/ x, for some positive constants ci, i. {1, 2, 3,4}.