Problem of the Week

Problem 22

Note that proof of this question requires knowledge of limits.
Let $f(x)$ be a continuous function.
It is given that $f(0) > 0$
Can you find a function $f(x)$ such that $f(x+y)$ = $f(x)f(y)$
(Note that x and y are just inputs into $f(x)$ . i.e: if $f(x) = 2x$ , $f(x+y) = 2x \cdot 2y$ )

Can you find the general solution to $f(x)$ ?
[Hint: use limits and $f(0)$ ]