What is F x and G x?
Simply so, what is difference between F x and G x?
g(x) just identifies a function of x, in the same way as that f(x) does. Using a "g" instead of an "f" only means the function has a different label assigned to it. Typically this is done where you have already got an f(x), so creating another one would be confusing.
Correspondingly, does G x mean X?
g(x) =2x or h(x) =2x,,,,,mean the same thing,,,except the axis is now g(x),,or h(x). The advantage of using functional notation is that different items can be differentiated, and still shown to be a function of x.
This is written as "( f o g)(x)", which is pronounced as "f-compose-g of x". And "( f o g)(x)" means " f (g(x))". That is, you plug something in for x, then you plug that value into g, simplify, and then plug the result into f.