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The domain of the function f given by f x = 1 x 2 - x - 6 is

Options

  1. A- ∞ , - 2
  2. B- ∞ , - 2 ∪ 4 , ∞
  3. C4 , ∞
  4. D- ∞ , - 2 ∪ 4 , ∞

Correct answer

B. - ∞ , - 2 ∪ 4 , ∞

Step-by-step solution

Given that f x = 1 x 2 - x - 6 > 0 , f is defined if x 2 - x - 6 > 0 or x - 3 x + 2 > 0 , ⇒ x < - 2 or x > 3 ⇒ x < - 2 or x ≥ 4 Hence, domain = - ∞ , - 2 ∪ 4 , ∞

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