Question 5
Let $f,g:\mathbb R\to\mathbb R$ satisfy $f(0)=2022$ and
$$f(x+g(y))=xf(y)+(2023-y)f(x)+g(x)\quad(x,y\in\mathbb R).$$
a) Prove that $f$ is surjective and $g$ is injective.
b) Find all pairs of functions $f,g$ satisfying the conditions.
$$f(x+g(y))=xf(y)+(2023-y)f(x)+g(x)\quad(x,y\in\mathbb R).$$
a) Prove that $f$ is surjective and $g$ is injective.
b) Find all pairs of functions $f,g$ satisfying the conditions.