Question

find f(g(x)) and g(f(x)) and determine whether each pair of functions f and g are inverses of each other.

Answer 1

So, if f(x)= 3x + 8 and g(x) = (x - 8)/3, replace f(g(x)) with the g(x).
Doing this will give you f(x-8/3). You plug this into what f(x) equals.
You should get f(x-8/3)= 3(x-8/3)+8. This will simplify to f(x-8/3)= x-8+8
So your answer, I guess, will be f(x-8/3)=x. I know the answer isn't a number like one would want, but this is how you do it correctly, as far as I know. You should use the same method for the g(f(x)), too.
I'll work out the g(f(x)) just in case you need to check your work.
So put 3x + 8 in for the f(x) in the g(f(x)). This will give you g(3x + 8). (btw, The reason why you then put it in for x is because you replace it for the x in the g(x), that means that whatever takes x's place is x. Just in case it's a little confusing, idk how much you've studied this  :D).
 After this, plug in the 3x + 8 for x, so you'll get g(3x +8)= [(3x +8) - 8]/3
This will simplify to 3x/3 which is also x.