Find all function $f:N_{0}\rightarrow N_{0}$ such that $$f(f(n))+f(n)=2n+6$$
Prove that for any $k\in\mathbb{N_0}$
$$f(n)\le \frac{\Big(\dfrac{16}{3}\cdot 4^k+\dfrac{2}{3}\Big)n+\dfrac{2}{3}(4^{k+2}+6k+11)}{\Big(\dfrac{16}{3}\cdot 4^k-\dfrac{1}{3}\Big)}$$