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The domain of the function f x = sec - 1 3 x - 4 + tan h - 1 x + 3 5 is

Options

  1. A- 8 , 1 ∪ 5 3 , 2
  2. B1 , 5 3
  3. C- 8 , 1 ∪ 5 3 , 2
  4. D( - 8 , 1 ] ∪ 5 3 , 2

Correct answer

D. ( - 8 , 1 ] ∪ 5 3 , 2

Step-by-step solution

Given that f x = sec - 1 3 x - 4 + tan h - 1 x + 3 5 Domain of sec - 1 x x   ∈   ( - ∞ , - 1 ]   ∪ [ 1 , ∞ ) sec - 1 3 x - 4 is ⇒ 3 x - 4   ∈ ( - ∞ , - 1 ]   ∪ [ 1 , ∞ ) ⇒ 3 x   ∈ ( - ∞ , 3 ] ∪ [ 5 , ∞ ) ⇒ x   ∈ ( - ∞ , 1 ] ∪ 5 3 , ∞       . . . ( I ) We know that domain of tan h - 1 x is - 1 , 1 ⇒ x + 3 5   ∈ - 1 , 1 ⇒ x + 3 &#160

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