For x R , let ^ -1 (x) (- 2 , 2 ). Then the minimum value of the function f: R R defined by f(x) = _0^ x ^ -1 x e^ (t - t) 1 + t^ 2023 ,dt is _____.

JEE Advanced 2023 Mathematics question

For , let . Then the minimum value of the function defined by is .

Answer: 0

for every real (both factors have the same sign), with equality only at . For

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Question ID VK-034120