Hi, I need help on these two problems dealing with functional equation
Let f be a function defined everywhere on the real axis. Suppose also that f satisfies the functional equation
f(x+y) = f(x)f(y) for all x and y.
A) Using only the functional equation, prove that f(0) is either 0 or 1. Also, prove that if f(0) then f(x) is not equal to 0 for all x.