Let \(A=\left[a_{i j}\right]\) be a \(3 \times 3\) matrix, where \( a_{i j}=\left\{\begin{array}{cc} 1, & \text { if…

Let \(A=\left[a_{i j}\right]\) be a \(3 \times 3\) matrix, where
\(
a_{i j}=\left\{\begin{array}{cc}
1, & \text { if } i=j \\
-x, & \text { if }|i-j|=1 \\
2 x+1, & \text { otherwise }
\end{array}\right.
\)

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

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