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JEE Main20199 Jan 2019Morning ShiftMathematicsFunctionsActual

For x ∈ R - 0 , 1 , let f 1 x = 1 x , f 2 x = 1 - x and f 3 x = 1 1 - x be three given functions. If a function, J x satisfies f 2 o J o f 1 x = f 3 x then J x is equal to:

Options

  1. Af 3 x
  2. B1 x f 3 x
  3. Cf 1 x
  4. Df 2 x

Correct answer

A. f 3 x

Step-by-step solution

Given f 2 J f 1 x = f 3 x ⇒ f 2 J 1 x = 1 1 - x ⇒ 1 - J 1 x = 1 1 - x ⇒ J 1 x = 1 - 1 1 - x = - x 1 - x ⇒ J x = - 1 x 1 - 1 x = - 1 x - 1 = 1 1 - x ∴   J x = f 3 x

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