And what are those circumstances you are asking? Well, this is going to be true if and only if two things are true. First of all, this limit needs to exist. So the limit as x approaches a of g of x needs to exist. So that needs to exist. And then on top of that, the function f needs to be continuous at this point, and f continuous at L. So let's look at some examples and see if we can apply this idea, or see if we can't apply it. So here I have two functions that are graphically represented right over here.