I've started studying functions and I am having trouble with the following question:
Find all solutions to the functional equation $f(x) +f(x+y)=y+2 $
Using the substitution technique when $y=0$ I have $f(x)=1$.
This implies that also $f(x+y)=1 $ and since $f(x)+f(x+y)=y+2$ , I am left with the conclusion that there are not solutions for the above functional equation.
Is this correct ?