WEBVTT
1
00:00:03.240 --> 00:00:05.719 A:middle L:90%
here we have the functions F, g and H
2
00:00:05.730 --> 00:00:07.580 A:middle L:90%
, and we're going to find the composition f of
3
00:00:07.580 --> 00:00:10.089 A:middle L:90%
G of h. Another way to write that is
4
00:00:10.089 --> 00:00:12.750 A:middle L:90%
with parentheses, f of G of h of X
5
00:00:13.609 --> 00:00:14.910 A:middle L:90%
. And when we read it that way we can
6
00:00:14.910 --> 00:00:17.820 A:middle L:90%
see that H is the inside function. It's going
7
00:00:17.820 --> 00:00:20.239 A:middle L:90%
to be substituted into G. So we're going to
8
00:00:20.239 --> 00:00:23.070 A:middle L:90%
take the cube root of X and we're going to
9
00:00:23.070 --> 00:00:25.730 A:middle L:90%
substituted into G. In both places, we see
10
00:00:25.730 --> 00:00:28.649 A:middle L:90%
an X that gives us G of h of X
11
00:00:29.239 --> 00:00:31.710 A:middle L:90%
. So G of h of X is the cube
12
00:00:31.710 --> 00:00:34.990 A:middle L:90%
root of X over the cube root of X minus
13
00:00:34.990 --> 00:00:38.950 A:middle L:90%
one. So that whole thing goes inside of death
14
00:00:39.439 --> 00:00:41.649 A:middle L:90%
. So we take that whole thing and we substituted
15
00:00:41.649 --> 00:00:44.320 A:middle L:90%
in to the F function in place of X.
16
00:00:44.840 --> 00:00:48.600 A:middle L:90%
And that's going to result in the tangent of that
17
00:00:48.600 --> 00:00:51.729 A:middle L:90%
Hubert of X, over the cube root of X
18
00:00:51.950 --> 00:00:52.750 A:middle L:90%
minus one