Quick, but hardish function problem

Test Preparation SAT Preparation
1

<p>So it goes like this:
For the function f, f(x+y)=f(x)*f(y) for all avlues of x and y. If f(x)>0 for all values of x, what is the value of f(0)?
A 0
B (sqrt2)/2
C 1
D sqrt2
E 4</p>

<p>The answer is C, but why?</p>

<p>EDIT: And another:
What is the hundreds digit of 11!<em>12!</em>13!<em>14!</em>15!*?
(student produced)</p>

2

<p>f(x) = f(0)
f(0 + y) = f(x) * f(y)
f(y) = f(x) * f(y)
1 = f(x)
f(0) = 1
C</p>