Given:
g(n) varies inversely with n
so,
[tex]\begin{gathered} g(n)\propto\frac{1}{n} \\ g(n)=\frac{k}{n} \end{gathered}[/tex]Where (k) is the proportionality constant
We will find the value of (k) using the given condition
When n = 2, g(n) = 11
Substitute with n and g(n)
[tex]11=\frac{k}{2}\rightarrow k=22[/tex]So, the relation between g(n) and (n) will be:
[tex]g(n)=\frac{22}{n}[/tex]We will find the value of (n) when g(n) = 8
So, substitute with g(n):
[tex]\begin{gathered} 8=\frac{22}{n} \\ \\ n=\frac{22}{8}=2.75 \end{gathered}[/tex]Rounding the answer to the nearest tenth
so, the answer will be:
[tex]n=2.8[/tex]