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

Question

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, 2, 3, 0, 4

MARKS App · Accepted Answer

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