first we establish that f(0)=0 since f(a+0)=f(a)=f(a)+f(0)
if we take a = 1 and b = 2007, then f(1)+f(2007) = f(2008) = 3012, then we can say f(1)+(f(1)+f(2006)) = f(2008), and go on until we get 2008*f(1) = f(2008) = 3012. then similarly we can see f(2009) = 1009*f(1)=2009*\frac{3012}{2008}=3013.5
OPTION C