Let A = [a ij ] be a 3 × 3 matrix, where a ij = \ 1, if i = j - x, if | i - j | = 1 2x + 1, otherwise.. Let a function f: R → R be defined as f(x) = det(A). Then the sum of maximum and minimum values of f on R is equal to:

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 20 Jul, Morning shift · Q2655

JEE Main 202120 Jul, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

A = [{a_{ij}}]

be a 3

\times

3 matrix, where

{a_{ij}} = \left\{ {\matrix{ 1 & , & {if\,i = j} \cr { - x} & , & {if\,\left| {i - j} \right| = 1} \cr {2x + 1} & , & {otherwise.} \cr } } \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: