Question 1085052
f(x+3) = f(x) + f(3), it means that f is a linear transformation.

so if f(x) = ax +b, 

f(x+3) = a(x+3) + b = ax +3a +b

f(3) = 3a + b.

So if f(x+3) = f(x) + f(3)

      ax+3a+b = ax +b +3a +b

So b=0, and a any real number.

Answer: f(x) = ax with a any real number. 

@natolino_