In order to find the inverse of the function f(n), we just need to switch f(n) by n, and switch n by f^-1(n) in the function. Then, we isolate f^-1(n). So we have that:
[tex]\begin{gathered} f(n)=-\frac{3}{n+1}+1 \\ n=-\frac{3}{f^{-1}(n)+1}+1 \\ -\frac{3}{f^{-1}(n)+1}=n-1 \\ \frac{3}{f^{-1}(n)+1}=1-n \\ 3=(f^{-1}(n)+1)(1-n) \\ f^{-1}(n)+1=\frac{3}{1-n} \\ f^{-1}(n)=\frac{3}{1-n}-1 \end{gathered}[/tex]So the inverse of f(n) is 3/(1-n) - 1
