00:01
So here we are considering the function e to the power of 2x minus 6e to the power of x.
00:14
So in a sense, f of x is really composed of like two potential functions, right? so we'll just call g of x equal to e to the power of 2x.
00:30
Okay, then that gives us that g prime is equal to 2e to 2e to, the power of 2x, which is 2 times g of x.
00:42
So that means g prime of x minus 2 times g of x is going to be equal to 0.
00:57
So the operator d minus 2 on this function g will be 0.
01:05
So keep that in mind as we take a look at this other sub function in f.
01:10
So let's call, let's not call it g again, that makes no sense, let's call it h of x, and we'll set that equal to negative 6e to the power of x.
01:28
Okay, well, h prime of x is equal to negative 6e to the power of x.
01:36
So that would mean that h prime of x minus h of x, right, because this is really as equal to h of x, is going to be equal to zero.
01:49
So here, our operator d minus 1 on h will be equal to 0.
02:00
Okay.
02:02
So how is that useful? so first, if we take, say, d minus 2 on f, what we get is really d minus 2 on f plus g, sorry, on g plus h...