Answer: Option B
2 is NOT in the domain of f ° g
Step-by-step explanation:
First we must perform the composition of both functions:
If [tex]g(x) = \sqrt{x-9}[/tex] and not [tex]\sqrt{x} -9[/tex]
[tex]f (x) = 4x + 3\\\\g (x) = \sqrt{x-9}\\\\f (g (x)) = 4 (\sqrt{x-9}) + 3[/tex]
The domain of the composite function will be all real numbers for which the term that is inside the root is greater than zero. When x equals 2, the expression within the root is less than zero
[tex]f (g (x)) = 4 (\sqrt{2-9}) + 3\\\\f (g (x)) = 4 (\sqrt{-7}) + 3[/tex]
The root of -7 does not exist in real numbers, therefore 2 does not belong to the domain of f ° g
The answer is Option B.
Note. If [tex]g(x) = \sqrt{x}-9[/tex]
So
[tex]f(g(x)) = 4(\sqrt{x})-36 + 3[/tex] And 2 belongs to the domain of the function
