00:01
All right, so this question is asking us, if the order is reversed when composing two functions, can the result ever be the same as the answer in the original order of the composition? if yes, give that example.
00:09
If no, explain why not.
00:11
So the simple answer is, yes, it is possible to have f of g, or f composed with g equal to g composed with f.
00:26
And the way that we're going to make that happen is if they are essentially undue each other.
00:31
So the example that we are going to be working with is f of x equal to x plus two, and g of x equal to x minus 2.
00:55
So you may see what i mean by undoing of each other.
00:59
So first we're to calculate f composed with g.
01:06
We solve this by replacing x with g of x.
01:10
So we see this x and f of x.
01:12
We replace it with x minus two.
01:19
We replace the x of f of x and we continue on with f of x and we add the two that's in fx.
01:27
So this will simplify...