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For a suitably chosen real constant a , let a function, f : R - - a → R be defined by f x = a - x a + x . Further supposed that for any real number x ≠ - a , and f ( x ) ≠ - a , fof x = x . Then f - 1 2 is equal to :

Options

  1. A1 3
  2. B- 1 3
  3. C- 3
  4. D3

Correct answer

D. 3

Step-by-step solution

f o f ( x ) = a - f x a + f ( x ) = x ⇒ a - a x 1 + x = f ( x ) ⇒ a ( 1 - x ) 1 + x = a - x a + x ( ∵ a = 1 ) so f ( x ) = 1 - x 1 + x f - 1 2 = 3

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