If $f(x)$ is odd function and $f(1) = a$, and $f(x + 2) = f(x) + f(2)$ then the value of $f(3)$ is

Since $f(x)$ is odd, $f(0)=0$ and $f(-x)=-f(x)$. Using the given relation with $x=0$ gives $$f(2)=f(0)+f(2).$$ This is consistent with $f(0)=0$. Now use the relation with $x=-1$: $$f(1)=f(-1)+f(2).$$ Because the function is odd, $$f(-1)=-f(1)=-a.$$ Also $f(1)=a$. So $$a=-a+f(2).$$ Hence $$f(2)=2a.$$ Now put $x=1$ in the relation: $$f(3)=f(1)+f(2).$$ Therefore $$f(3)=a+2a=3a.$$ Matching with the options, the correct choice is $D$.