f(0) = f(0+0) = f(0)*f(0) = [f(0)]^2

so we have f(0) = [f(0)]^2

=> [f(0)]^2 - f(0) = 0

=> f(0)[f(0) - 1] = 0

=> f(0) = 0 or f(0) - 1 = 0

=> f(0) = 0 or f(0) = 1

i believe a part of this question is missing. "if f(0) is what? then f(x) is not equal to 0 for all x."Also, prove that if f(0) then f(x) is not equal to 0 for all x.