Respuesta :

mhanifa

Answer:

  • Option D

Step-by-step explanation:

Given:

  • f(x) = 1/ (x - 3)
  • g(x) = [tex]\sqrt{x+5}[/tex]

The composite function f · g(x) is:

  • f(g(x)) = 1 / ( [tex]\sqrt{x+5} - 3[/tex])

Restrictions are:

  • x + 5 ≥ 0 ⇒ x ≥ - 5

and

  • [tex]\sqrt{x+5}[/tex] ≠ 3 ⇒ x + 5 ≠ 9 ⇒ x ≠ 4

Combination of the above gives us the domain:

  • x ∈ [ - 5, 4) ∪ (4, +∞)

Correct choice is D

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