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The domain of the function f x = x 2 - 8 x + 12 . ln 2 ⁡ x - 3 is

Options

  1. A3 , ∞
  2. B4 , ∞
  3. C6 , ∞ ∪ 2,4
  4. D6 , ∞ ∪ 4

Correct answer

D. 6 , ∞ ∪ 4

Step-by-step solution

x 2 - 8 x + 12 ln 2 x - 3 ≥ 0 and x - 3 > 0 ⇒ x 2 - 8 x + 12 ≥ 0 ⇒ x ∈ ( - ∞ , 2 ] ∪ [ 6 , ∞ ) Also, ln x - 3 = 0 ⇒ x = 4 Hence, the solution is x ∈ 4 ∪ [ 6 , ∞ )

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