# Math Help - functions

1. ## [SOLVED] functions

The function $f$ has the property that $f(x)+f(y)= (x+y)f(xy)$ for all non-zero real numbers $x$ and $y$ . A possible rule for $f$ is

A. $f(x)=2x$

B. $f(x)=5-2x$

C. $f(x) = \frac{1}{x}$

D. $f(x)= e^x$

E. $f(x)=\ln x$

I can expand every option out. But I'm having a lazy day. Is there an easier way?

2. C. is the answer. Just lazy I am.

3. I don't think so. I've been thinking but I can't express the property in natural terms that do not require expanding each function to see if it matches.