Answer: B) F(x) = √x and G(x) = 3x + 2
Step-by-step explanation:
The composite function G(F(x)) is when you replace every x-value in the G(x) function with the F(x) function.
[tex]A)\ G(3x+2) = \sqrt{3x+2}\\\\B)\ G(\sqrt{x})=3(\sqrt{x})+2\quad =3\sqrt{x}+2\\\\C)\ G(\sqrt{x}+2) = 3\quad \text{there are no x-values in the G(x) function to replace}\\\\D) G(3\sqrt{x})=2\quad \text{there are no x-values in the G(x) function to replace}[/tex]
The only one that matches G(F(x)) = 3√x + 2 is OPTION B
