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Let f : R → R be such that for all x ∈ R 2 1 + x + 2 1 - x , f x and 3 x + 3 - x are in A.P., then the minimum value of f x is

Options

  1. A2
  2. B3
  3. C0
  4. D4

Correct answer

B. 3

Step-by-step solution

f x = 2 1 - x + 2 1 + x + 3 x + 3 - x 2 ⇒ f x = 2 3 - x + 3 x + 3 x + 3 - x 2 ⇒ f x = 3 - x + 3 x + 3 x + 3 - x 2 Using A M ≥ G M f x ≥ 3

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