WEBVTT
1
00:00:02.940 --> 00:00:05.059 A:middle L:90%
here we have the function R of X, and
2
00:00:05.059 --> 00:00:07.339 A:middle L:90%
we're going to think of it as a composition f
3
00:00:07.339 --> 00:00:09.859 A:middle L:90%
of G of h. Another way to write that
4
00:00:09.859 --> 00:00:12.849 A:middle L:90%
would be f of G of h of X.
5
00:00:14.390 --> 00:00:16.609 A:middle L:90%
So basically, we want to figure out what f
6
00:00:16.620 --> 00:00:19.609 A:middle L:90%
g and h r To make this work. H
7
00:00:19.609 --> 00:00:23.010 A:middle L:90%
will be the innermost function. And the innermost function
8
00:00:23.010 --> 00:00:25.289 A:middle L:90%
we see is the square root of X. So
9
00:00:25.289 --> 00:00:28.769 A:middle L:90%
let's let h of x equals the square root of
10
00:00:28.769 --> 00:00:32.149 A:middle L:90%
X. Now we need the middle A or G
11
00:00:32.840 --> 00:00:35.310 A:middle L:90%
G would be what h of x was plugged into
12
00:00:35.939 --> 00:00:38.679 A:middle L:90%
. So if we let g of x b X
13
00:00:38.679 --> 00:00:41.520 A:middle L:90%
minus one, we could see that if we were
14
00:00:41.520 --> 00:00:45.719 A:middle L:90%
to calculate G of h of X, we would
15
00:00:45.719 --> 00:00:49.570 A:middle L:90%
get square root of X minus one. So that's
16
00:00:49.579 --> 00:00:53.179 A:middle L:90%
inside the outside radical. So that means the outermost
17
00:00:53.179 --> 00:00:57.840 A:middle L:90%
function f is the outside radical. We'll call that
18
00:00:57.840 --> 00:01:00.119 A:middle L:90%
square Rydex. So you see, if we were
19
00:01:00.119 --> 00:01:03.149 A:middle L:90%
to put G of h of X inside a bath
20
00:01:06.340 --> 00:01:07.109 A:middle L:90%
, we would be putting the square root of X
21
00:01:07.109 --> 00:01:11.799 A:middle L:90%
minus one inside a square root. And that was
22
00:01:11.799 --> 00:01:12.280 A:middle L:90%
our goal. That was what we were trying to
23
00:01:12.280 --> A:middle L:90%
get