Question 83
Consider the function $f: \mathbb{R}^{+} \to \mathbb{R}^{+}$ and satisfying
$$
f(x + 2y + f(x + y)) = f(2x) + f(3y), \forall x, y \gt 0.
$$
1. Find all functions $f(x)$ that satisfy the given condition.
2. Suppose that $f(4\sin^4x)f(4\cos^4x) \ge f^2(1)$ for all $x \in (0; \frac{\pi}{2})$. Find the minimum value of $f(2022)$.
$$
f(x + 2y + f(x + y)) = f(2x) + f(3y), \forall x, y \gt 0.
$$
1. Find all functions $f(x)$ that satisfy the given condition.
2. Suppose that $f(4\sin^4x)f(4\cos^4x) \ge f^2(1)$ for all $x \in (0; \frac{\pi}{2})$. Find the minimum value of $f(2022)$.