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The domain of the function f x = 1 9 - x 2 + l o g 20 x 3 - 3 x is

Options

  1. A- 3 , 0 ∪ 3 , ∞
  2. B- 3 , 0 ∪ 3 , 3
  3. C- 3 , 0 ∪ 3 , ∞
  4. D- 3 , 0 ∪ 3 , 3 ∪ 3 , ∞

Correct answer

D. - 3 , 0 ∪ 3 , 3 ∪ 3 , ∞

Step-by-step solution

9 - x 2 ≠ 0 and x 3 - 3 x > 0 x ≠ - 3 , 3 .... ( 1 ) and x x 2 - 3 > 0 ⇒ x x + 3 x - 3 > 0 x ∈ - 3 , 0 ∪ 3 , ∞ …. 2 From 1 ∩ 2 , we get, x ∈ - 3 , 0 ∪ 3 , 3 ∪ 3 , ∞

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