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AP EAMCET202120 Aug 2021Evening ShiftMathematicsFunctionsActual

Let f x = x + 2 2 - 2 , x ≥ - 2 . Then f - 1 x =

Options

  1. A- 2 + x - 2
  2. B2 + x + 2
  3. C2 + x - 2
  4. D- 2 + x + 2

Correct answer

C. 2 + x - 2

Step-by-step solution

Let f x = x + 2 2 - 2 , x ≥ - 2 . Putting y = x + 2 2 - 2 y = x 2 + 4 x + 4 - 2 y = x 2 + 4 x + 2 x 2 + 4 x + 2 - y = 0 a = 1 ,   b = 4 ,   c = 2 - y x = - 4 ± 4 2 - 4 × 1 × 2 - y 2 × 1 x = - 4 ± 16 - 8 + 4 y 2 × 1 Then, x = - 2 + 2 + y , x ≥ - 2 Hence, f - 1 x = 2 + x - 2

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