Can't seem to find the lower bound for this function

Question

Been reading about algorithms. I am trying to find the lower and upper bounds for the function f(n). not very familiar with mathjax so i used mathtype. how do i proceed with the lower bound. especially the denominator.

also, is the upper bound $24n$ the tightest possible bound ?

Answer 1

An bound for $f$ is simply $$ \frac{19}{5}n \le f(n)\le \frac{19}{5}n + 1 $$ for all $n\ge 1$. This follows from $0\le 1-\frac{1}{n}\le 1$. Usually for the algorithm one just says that $f$ is in $O(n)$. So you could also take any estimate like $f(n)\le 10^6n$ for all $n\ge 1$.