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JEE Main202324 Jan 2023Evening ShiftMathematicsFunctionsActual

If f x = 2 2 x 2 2 x + 2 , x ∈ R , then f 1 2023 + f 2 2023 + f 3 2023 . . . . . . . . . f 2022 2023 is equal to

Options

  1. A2011
  2. B1010
  3. C2010
  4. D1011

Correct answer

D. 1011

Step-by-step solution

Given, f x = 2 2 x 2 2 x + 2 , so f 1 - x = 2 2 - 2 x 2 2 - 2 x + 2 = 2 2 2 2 + 2 2 x + 1 = 2 2 + 2 2 x Now f x + f 1 - x = 2 2 x 2 2 x + 2 + 2 2 + 2 2 x = 1 So by using the relation f x + f 1 - x = 1 we will solve the given equation f 1 2023 + f 2 2023 + f 3 2023 . . . . . . . . . f 2022 2023 = f 1 2023 + f 2022 2023 + f 2 2023 + f 2021 2023 + f 3 2023 + f 2020 2023 . . . . . . . . . f 1011 2023 + f 1012 2023 = f 1 2023 + f 2022 2023 ⏟ 1 + f 2 2023 + f 2021 2023 ⏟ 1 + f 3 2023 + f 2020 2023 ⏟ 1 .

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