Let \(A=\left[{a}_{ij}\right]\) be a \(3\times 3\) matrix, where \({a}_{ij}=\left{\begin{matrix}1,\text{ if }i=j \\ -x,\…

Let \(A=\left[{a}_{ij}\right]\) be a \(3\times 3\) matrix, where

\({a}_{ij}=\left{\begin{matrix}1,\text{ if }i=j \\ -x,\text{ if }|i-j|=1 \\ 2x+1,\text{ otherwise }\end{matrix}\right.\)

Let a function \(f:R\to R\) be defined as \(f(x)=\det (A)\). Then the sum of maximum and minimum values of f on R is equal to :

[JEE Main 2021, 20 Jul (Shift 1)]