Question 75
Find all functions $f: \mathbb{Z}^{+} \rightarrow \mathbb{Z}^{+}$ such that
$$
n^{3}-n^{2} \leq f(n) \cdot (f(f(n)))^{2} \leq n^{3}+n^{2}
$$
for every $n$ is positive integers.
$$
n^{3}-n^{2} \leq f(n) \cdot (f(f(n)))^{2} \leq n^{3}+n^{2}
$$
for every $n$ is positive integers.