Let f be a real valued function, defined on R - - 1 , 1 and given by f x = 3 log e x - 1 x + 1 - 2 x - 1 .…

Let f be a real valued function, defined onR--1,1 and given by fx=3logex-1x+1-2x-1. Then in which of the following intervals, function fx is increasing?

  1. -∞,-1∪12,∞-1

  2. -∞,∞--1,1
  3. -1,12
  4. -∞,12--1

Solution

fx=3logex-1-3logex+1-2x-1

f'x=3x-1-3x+1+2x-12

f'x=42x-1x-12x+1

f'x≥0

⇒  x∈-∞,-1∪12,1∪1,∞ or -∞,-1∪12,∞-1

Asked in: JEE Main 2021 (16 Mar Shift 2)

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