the letter which you use to label a function has no special meaning. 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.
you can use any letter you like (i wouldn't use x, though):
f(x) = 2x+1
g(x) = 100x^2
r(x) = 10+6x
Now, we could have called all of those f(x), but it woudl get pretty confusing if you ever had a problem involving more than one of those at a time!