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…

Let f:R→R be such that for all x∈R21+x+21-x, fx and 3x+3-x are in A.P., then the minimum value of fx is
  1. 2
  2. 3
  3. 0
  4. 4

Solution

fx=21-x+21+x+3x+3-x2

⇒fx=23-x+3x+3x+3-x2

⇒fx=3-x+3x+3x+3-x2


Using AM≥GM
fx≥3

Asked in: JEE Main 2020 (08 Jan Shift 1)

Practice more Sequences and Series questions on Aicharya