When dealing with inverse functions, I like to put them in terms of x and y to make it easier. y=3x-2 and y=-1/3x+2/3
to find the inverse of a function, one method is to switch the variables and then solve for the same variable as the first time, so the inverse of y=3x-2 is x=3y-2, which we now solve for y again.
x=3y-2 => x+2=3y => y=1/3x+2/3 which is not the same as y=-1/3x+2/3
Final answer:
No, f(x) and g(x) are not inverse functions.
Hope I could help :)