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JEE Main202126 Feb 2021Evening ShiftMathematicsFunctionsActual

Let f x = sin - 1 x and g x = x 2 - x - 2 2 x 2 - x - 6 . If g 2 = lim x → 2 g x , then the domain of the function f o g is

Options

  1. A( - ∞ , - 1 ] ∪ [ 2 , ∞ )
  2. B( - ∞ , - 2 ] ∪ - 3 2 , ∞
  3. C( - ∞ , - 2 ] ∪ - 4 3 , ∞
  4. D( - ∞ , - 2 ] ∪ [ - 1 , ∞ )

Correct answer

C. ( - ∞ , - 2 ] ∪ - 4 3 , ∞

Step-by-step solution

Domain of f o g x = sin - 1 g x ⇒ g ( x ) ≤ 1 , g 2 = 3 7 x 2 - x - 2 2 x 2 - x - 6 ≤ 1 x + 1 x - 2 2 x + 3 x - 2 ≤ 1 x + 1 2 x + 3 ≤ 1 and x + 1 2 x + 3 ≥ - 1 x + 1 - 2 x - 3 2 x + 3 ≤ 0 and x + 1 + 2 x + 3 2 x + 3 ≥ 0 x + 2 2 x + 3 ≥ 0 and 3 x + 4 2 x + 3 ≥ 0 x ∈ ( - ∞ , - 2 ] ∪ - 4 3 , ∞

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