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JEE Main202229 Jul 2022Evening ShiftMathematicsFunctionsActual

The domain of the function f x = sin - 1 x 2 - 3 x + 2 x 2 + 2 x + 7 is

Options

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

Correct answer

C. [ - 1 , ∞ )

Step-by-step solution

Given, f x = sin - 1 x 2 - 3 x + 2 x 2 + 2 x + 7 We know that domain of sin - 1 f x is - 1 ≤ f x ≤ 1 So, x 2 - 3 x + 2 x 2 + 2 x + 7 ≥ - 1 and x 2 - 3 x + 2 x 2 + 2 x + 7 ≤ 1 Now solving x 2 - 3 x + 2 x 2 + 2 x + 7 ≥ - 1 Since denominator x 2 + 2 x + 7 is always positive, So, x 2 - 3 x + 2 ≥ - x 2 + 2 x + 7 ⇒ 2 x 2 - x + 9 ≥ 0 ⇒ x ∈ R   . . . . . 1 Now solving x 2 - 3 x + 2 x 2 + 2 x + 7 ≤ 1 ⇒ x 2 - 3 x + 2 ≤ x 2 + 2 x + 7 ⇒ 5

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