The question is:

f is a function defined on $\displaystyle Z$. Assume that f satisfies the following properties:

f(0) doesn't equal 0

f(1) equals 3

f(x) * f(y) = f(x+y) + f(x-y)

1. Determine f(7).

2. Prove that f(n)=f(-n) for all integers n.

...I'm not sure even how to begin with this problem. Does anyone have any hints to get me started??? I'm sure after that I'll be fine. Thanks