1. ## functions

can someone help me out with this question?

f(xy)=f(x)f(y), f(0) does not equal 0. Find the value of f(2003).

2. ## Re: functions

Note that $f(0) = f(0)f(0)$. Since $f(0) \neq 0$, $f(0) = 1$.

Hence, for any k, $f(0k) = f(k)f(0) \Rightarrow 1 = f(k)(1) \Rightarrow f(k) = 1$ for all k. Therefore, $f(2003) = 1$.