How find this function $f(x)$ such $f(a+f(b))=f(a+b)+f(b)$ let function $f:R_{+}\to R_{+}$,and such
$$f(a+f(b))=f(a+b)+f(b),\forall a,b\in R_{+}$$
Find $f(x)$.
my try: let $a=b=1$,then 
$$f(1+f(1))=f(2)+f(1)$$
$a=1,b=2$,then
$$f(1+f(2))=f(3)+f(2)$$
then I can't find have any regular,so I can't.Thank you
Edit: This is IMO2007 SL, Problem A4.

the hint is :
$f(f(2a))=f(a+f(a+f^{-1}(a)))=f(2a+f^{-1}(a))+a$
$f(2f(a))=f(f(a)+a)+f(a)=f(2a)+2a$
$\Longrightarrow$$f(2a)+a=f(2a+f^{-1}(a))$
$\Longrightarrow$$f(x)=2x$
