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JEE Main20231 Feb 2023Evening ShiftMathematicsFunctionsActual

Let f : R - 0 , 1 → R be a function such that f x + f 1 1 - x = 1 + x . Then f 2 is equal to :

Options

  1. A9 2
  2. B9 4
  3. C7 4
  4. D7 3

Correct answer

B. 9 4

Step-by-step solution

Given, f x + f 1 1 - x = 1 + x x = 2 ⇒ f 2 + f - 1 = 3                   … 1 x = - 1 ⇒ f - 1 + f 1 2 = 0         … 2 x = 1 2 ⇒ f 1 2 + f 2 = 3 2           … 3 On subtracting equation 3 and equation 2 we get, f ( 2 ) - f ( - 1 ) = 3 4   . . . . . . . . ( 4 ) On adding equation 1 and equation 4 we get, 2 f 2 = 9 2 ⇒   f 2 = 9 4

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