00:01
Right, so here we're given that f of x is 2 of x plus 1, and g of x is 2x squared minus 3.
00:08
And we are defined f -com, f little circle, g of 2, which is f -composition g of 2.
00:16
And then g -composition f of 2 here.
00:20
Over here is g -composition f of 2.
00:23
This is f -composition g of a negative 3, g -composition f of a negative 5, composition g of a, g composition f of a negative a, and then f composition f of 1, and g composition g of a negative 1.
00:43
So composition means you have to do this part of the first in all of them.
00:50
And then whatever you get for an answer, you use that in the other part.
00:58
And to visualize this even more.
01:01
Another way to write this, so we'll just use this one, f composition g of 2.
01:05
Another way to write that is f g of 2.
01:12
So we have to figure out that before we can figure out that.
01:17
Or even if we're in deciding if you're looking at this one.
01:20
That is g f negative 5.
01:27
So you have to do this part first so that you can use that to figure out that part.
01:36
And so to start with f composition g of 2.
01:43
So we have to substitute a 2.
01:45
N4 x so g of 2 is equal to 2 times 2 squared minus 3 and 2 squared is 4 times 2 is 8 minus 3 is 5 so now what is 5 of 5 all that is 2 times 5 plus 1 which is 11 so f composition g of 2 equals 11 over here, g composition f of 2.
02:27
First, we have to do f of 2, and that would be 2 times 2 plus 1, which is 5.
02:39
Now then when you substitute and figure out, hey, what's g of 5? that would be 2 times 5 squared minus 3.
02:52
Well, 5 squared is 25 times 2 is 50, and 50 minus 3 is 47.
02:59
So g composition f of 2 is 47.
03:09
Next question here.
03:11
F composition g of a negative 3.
03:14
So we have to substitute a negative 3 and first g of negative 3 is equal to 2 2 times negative 3 squared minus 3.
03:26
Negative 3 squared is 9.
03:30
9 times 2 is 18.
03:32
18 minus 3 is 15.
03:37
So then what is f of 15? well that would be two times 15 plus 1 and that's 30 plus 1 which is 31.
03:55
So f composite g of negative 3 is 31.
04:02
Over here g composition f of a negative 5.
04:08
So f of a negative 5 first and that would be 2 times a negative 5 plus 1.
04:20
And 2 times a negative 5 is a negative 10 plus 1 is a negative 9.
04:29
So now we have to do g of a negative 9.
04:33
And that will equal 2 times negative 9 squared minus 3.
04:44
Negative 9 squared is 81 .81 times 2 is 162 minus 3.
04:53
Would be 159.
05:01
Right.
05:01
F composition g of a...