Question

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

Answer 1

Answer:

second choice

Step-by-step explanation:

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

$= f(g(x))$

$= f(-7x + 7)$

$= \sqrt{-7x + 7 + 3}$

$= \sqrt{-7x + 10}$

Let x = 5:

$(f \circ g)(5) = \sqrt{-7(5) + 10}$

$(f \circ g)(5) = \sqrt{-35 + 10}$

$(f \circ g)(5) = \sqrt{-25}$

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