Let $f:\mathrm{ℝ}\to \mathrm{ℝ}$ be defined as $f\left(x\right)=x-1$  and $g:R\to \left\{1,-1\right\}\to \mathrm{ℝ}$ be defined as $g\left(x\right)=\frac{x^2}{x^2-1}$. Then the function $fog$ is:

Let $S=\left\{1,2,3,4,5,6,7,8,9,10\right\}$. Define $f:S\to S$ as $f\left(n\right)=\left\{\begin{array}{cl}2n,& \mathrm{if} n=1,2,3,4,5\\ 2n-11& \mathrm{if} n=6,7,8,9,10\end{array}\right.$
Let $g:S\ge S$ be a function such that $fog\left(n\right)=\left\{\begin{array}{ll}n+1& , \mathrm{if} n \mathrm{is} \mathrm{odd} \\ n-1& , \mathrm{if} n \text{is }\mathrm{even} \end{array}\right.$,

then $g\left(10\right)\left[g\left(1\right)+g\left(2\right)+g\left(3\right)+g\left(4\right)+g\left(5\right)\right]$ is equal to