JEE Math Practice Question

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

1. A.$$ - {{20} \over {27}}$$
2. B.$${{88} \over {27}}$$
3. C.$${{20} \over {27}}$$
4. D.$$ - {{88} \over {27}}$$