Can you attack this function?

Algebra Level 4

If $f(x)=\frac{4^x}{4^x+2}$ , where $x€Q$ , then $f(\frac{1}{2007})+f(\frac{2}{2007})+...+f(\frac{2006}{2007})$ equals to $?$

1999 2016 none of them 1003 2015 2007