Question

Which of the following is the domain of the function G(F(x))?

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

Answer 1

Answer: 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) =
`√(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.