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JEE Main20208 Jan 2020Morning ShiftMathematicsFunctionsActual

The inverse function of f x = 8 2 x - 8 - 2 x 8 2 x + 8 - 2 x , x ∈ - 1 , 1 , is __________.

Options

  1. A1 4 log e 1 + x 1 - x
  2. B1 4 log e 1 - x 1 + x
  3. C1 4 log e log e 1 - x 1 + x
  4. D1 4 log 8 1 + x 1 - x

Correct answer

D. 1 4 log 8 1 + x 1 - x

Step-by-step solution

y = 8 2 x - 8 - 2 x 8 2 x + 8 - 2 x ⇒   1 + y 1 - y = 8 2 x 8 - 2 x (Applying componendo-dividendo) ⇒     8 4 x = 1 + y 1 - y ⇒     4 x = l o g 8 1 + y 1 - y f - 1 x = 1 4 l o g 8 1 + x 1 - x s

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