3. Find $g(2022)$, if for any real $x, y$ the equality holds

$$
g(x-y)=g(x)+g(y)-2021(x+y)
$$

#
# Answer: 4086462.

Solution. Substitute $x=y=0$, we get

$$
g(0)=g(0)+g(0)-2021(0+0) \Rightarrow g(0)=0
$$

Substitute $x=y$, we get

$$
\begin{gathered}
g(0)=g(x)+g(x)-2021(x+x) \Rightarrow g(x)=2021 x \Rightarrow \\
g(2022)=2021 \cdot 2022=4086462
\end{gathered}
$$