Answer:
second choice
Step-by-step explanation:
First, do the composition of the functions.
[tex] (f \circ g)(x) = f(g(x)) [/tex]
[tex] = f(\sqrt{x + 3}) [/tex]
[tex] (f \circ g)(x) = -8\sqrt{x + 3} - 4 [/tex]
Now we find (fog)(9).
[tex] (f \circ g)(9) = -8\sqrt{9 + 3} - 4 [/tex]
[tex] (f \circ g)(9) = -8\sqrt{12} - 4 [/tex]
[tex] (f \circ g)(9) = -16\sqrt{3} - 4 [/tex]
(fog)(9) evaluates to a real number, so 9 is in the domain of the composition of functions f and g.
Answer: second choice
