MathNet 2026 — Part 06 Question 80

Let $\mathbb{N}$ denote the strictly positive integers. A function $f : \mathbb{N} \to \mathbb{N}$ has the following properties which hold for all $n \in \mathbb{N}$:

(a) $f(n) \lt f(n + 1)$;

(b) $f(f(f(n))) = 4n$.
Find $f(2022)$.