Need explanation for CLRS Solution 3-3.

I am currently studying “Order of growth” from 3rd edition.
I was not able to understand the solution for the problem 3-3(b)
problem : Give an example of a single non-negative function f(n) such that for all functions g(n) in part (a), f(n) is neither O(g(n)) nor (g(n))…

On some places it is given as the solution is given as (1 + Sin(n))*2^2^(n+2)

If somebody can explain its derivation, that will be good.

I didn’t understand the question clearly here, Also I tried to search on cormen but I didn’t found this question.

Its exercise 3-3(b) in cormen 3rd edition, check in soft copy available online