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JEE Main202224 Jun 2022Morning ShiftMathematicsFunctionsActual

The domain of f x = cos - 1 x 2 - 5 x + 6 x 2 - 9 log x 2 - 3 x + 2 is

Options

  1. Ax ∈ - 1 2 , 1 ∪ 2 , ∞ - 3
  2. Bx ∈ - 1 2 , 1 ∪ 2 , ∞ - 3
  3. Cx ∈ - 1 2 , 1 ∪ 2 , ∞ - 3
  4. Dx ∈ - 1 2 , 1 ∪ 2 , ∞ - 3

Correct answer

A. x ∈ - 1 2 , 1 ∪ 2 , ∞ - 3

Step-by-step solution

We know that, cos - 1 x is defined when - 1 ⩽ x ⩽ 1 So, cos - 1 x 2 - 5 x + 6 x 2 - 9 is defined when - 1 ⩽ x 2 - 5 x + 6 x 2 - 9 ⩽ 1 and x 2 - 9 ≠ 0 ⇒ - 1 ≤ x - 3 x - 2 x - 3 x + 3 ≤ 1 and x ≠ ± 3 ⇒ - 1 ≤ x - 2 x + 3 ≤ 1 and x ≠ ± 3 , ⇒ - 1 ≤ x + 3 - 5 x + 3 ≤ 1 and x ≠ ± 3 ⇒ - 1 ≤ 1 - 5 x + 3 ≤ 1 and x ≠ ± 3 , ⇒ - 2 ≤ - 5 x + 3 ⩽ 0 and x ≠ &

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