If f and g are one-to-one functions on a set A, and for any elements x and y belonging to A if:

f(x)+f(y)=f(x+y) &

g(x)+g(y)=g(x+y)

is it true that f o g = g o f ? If so, please show why.

Otherwise what are sufficient conditions for any functions m and p to commute, i.e. m o p = p o m.