Question 89
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ that satisfy the conditions $f(0)\gt 0$ and
$$
f(x+y)=f(x) \cdot f(2022-y)+f(y) \cdot f(2022-x)
$$
for all $x, y \in \mathbb{R}$.
$$
f(x+y)=f(x) \cdot f(2022-y)+f(y) \cdot f(2022-x)
$$
for all $x, y \in \mathbb{R}$.