An index function question

It would be greatly appreciated if someone could show me how to figure this out:

A function f has the property f(x)*f(y) = 2f(x+y), what is a possible rule for f?
It's a multiple choice, and the answer is f(x) = 2e^x. The 2f(x+y) is the bit that confuses me.

Thanks!

f(x) = 2e^x

f(x)*f(y) = (2e^x)( 2e^y)
f(x)*f(y) = 4e^(x + y)..................(i)

2f(x+y) = 2{ 2e^(x + y) }
2f(x+y) = 4e^(x + y)..................(ii)

(i) = (ii)

f(x) = 2 e^x
so
f(y) = 2 e^y
f(x) f(y) = 4 e^x e^y = 4 e^(x+y) = 2(2 e^(x+y)) = 2 f(x+y)