Which of the following is the domain of the function g(f( f(x) = x + 4, g(y) = g(f(x)) = a. all numbers less than or equal to 4 b. all numbers less than or equal to -4 c. all numbers greater than or equal to -4 d. all numbers greater than or equal to 4

option C. all numbers greater than or equal to -4.

Justification:

1) G(F(x)) means apply first the rule F(x) and then apply the rule G(y) to the outcome of (Fx).

2) Mathematically that is:

G(F(x) = G (x + 4) =

3)  The the domain is all the numbers for which the expression inside the root are not negative, i.e x + 4 ≥ 0

⇒ x ≥ - 4

That is the option C. all number greater than or equal to - 4.