Answer:
second choice
Step-by-step explanation:
[tex] (f \circ g)(x) = [/tex]
[tex] = f(g(x)) [/tex]
[tex] = f(-7x + 7) [/tex]
[tex] = \sqrt{-7x + 7 + 3} [/tex]
[tex] = \sqrt{-7x + 10} [/tex]
Let x = 5:
[tex] (f \circ g)(5) = \sqrt{-7(5) + 10} [/tex]
[tex] (f \circ g)(5) = \sqrt{-35 + 10} [/tex]
[tex] (f \circ g)(5) = \sqrt{-25} [/tex]
Since using x = 5 gives the square root of a negative number, 5 is not in the domain of the composition of the functions.
Answer: second choice
