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JEE Main202329 Jan 2023Morning ShiftMathematicsFunctionsActual

The domain of f x = log x + 1 x - 2 e 2 log e x - 2 x + 3 , x ∈ R is

Options

  1. Aℝ - - 1 , 3
  2. B2 , ∞ - 3
  3. C- 1 , ∞ - 3
  4. Dℝ - 3

Correct answer

B. 2 , ∞ - 3

Step-by-step solution

Given, Function f x = log x + 1 x - 2 e 2 log e x - 2 x + 3 ,   x ∈ R To find domain we will take following cases: Case-1: x - 2 > 0 ⇒ x > 2 x ∈ 2 , ∞ Case-2: x + 1 > 0 ⇒ x > - 1 And, x + 1 ≠ 1 ⇒ x ≠ 0 x ∈ - 1 , 0 ∪ 0 , ∞ Case-3: x > 0 x ∈ 0 , ∞ Case-4: e 2 log e x - 2 x + 3 ⇒ x 2 - 2 x - 3 ≠ 0 ⇒ x - 3 x + 1 ≠ 0 x ≠ - 1 , 3 From case  ( 1 )   ∩   case  ( 2 )

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