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JEE Main20198 Apr 2019Morning ShiftMathematicsFunctionsActual

If f x = log e 1 - x 1 + x , x < 1 , then f 2 x 1 + x 2 is equal to

Options

  1. Af x 2
  2. B2 f x 2  
  3. C– 2 f x
  4. D2 f x

Correct answer

D. 2 f x

Step-by-step solution

f x = l n 1 - x 1 + x ⇒ f 2 x 1 + x 2 = l n 1 - 2 x 1 + x 2 1 + 2 x 1 + x 2 = l n 1 + x 2 - 2 x 1 + x 2 + 2 x = l n 1 - x 1 + x 2 = 2 l n 1 - x 1 + x = 2 l n 1 - x 1 + x             ∵ x < 1 = 2 f x

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