What can I do to this to make it independent of x. i.e. manipulate it somehow to cancel out the g(x)?
btw and
Take note of those absolute value signs that should be there.
To deal with this problem, you'll certainly need to know that N is not zero. Given that that is the case, suppose that you choose to be less than . By the triangle inequality, that will imply that g(x) lies between and . That should enable you to make some progress.