Answer: OPTION C.
Step-by-step explanation:
In order to solve the given exercise, you can follow these steps:
1. Given the following function f(x):
[tex]f(x)=\frac{x-2}{3}[/tex]
You must substitute [tex]x=2[/tex] into the function f(x). Then:
[tex]f(2)=\frac{(2)-2}{3}[/tex]
2. Evaluating, you get:
[tex]f(2)=\frac{0}{3}\\\\f(2)=0[/tex]
3. Now, the next step is to substitute [tex]f(2)[/tex] into the function g(x):
[tex]g (x) = 3x+2\\\\g (f(2)) = 3(0)+2[/tex]
4. Finally, evaluating, you get the following result:
[tex]g (f(2)) = 0+2\\\\g (f(2)) =2[/tex]
You can identify that it matches with the Option C.
