Question

Help Please, anyone good at domain values of composite functions.

Answer 1

Answer:

second choice

Step-by-step explanation:

First, do the composition of the functions.

$(f \circ g)(x) = f(g(x))$

$= f(\sqrt{x + 3})$

$(f \circ g)(x) = -8\sqrt{x + 3} - 4$

Now we find (fog)(9).

$(f \circ g)(9) = -8\sqrt{9 + 3} - 4$

$(f \circ g)(9) = -8\sqrt{12} - 4$

$(f \circ g)(9) = -16\sqrt{3} - 4$

(fog)(9) evaluates to a real number, so 9 is in the domain of the composition of functions f and g.

Answer: second choice