Answer
See below.
Work Step by Step
According to the rule of the exercise: $f(2)=f(1)+f(1)=6$, $f(3)=f(2)+f(1)=6+3=9$, $f(4)=f(3)+f(1)=9+3=12$.
$f(x+y)$ does not equal $f(x)+f(y)$ for all functions, e.g. for $f(x)=x^2$, $f(1)=1$, $f(2)=4$, $f(1)+f(2)=5\ne9=f(3)=f(2+1)$
