1
00:00:00,979 --> 00:00:05,928
f(x) = 9 - x squared

2
00:00:05,928 --> 00:00:09,062
and g(x) = 5 times x squared

3
00:00:09,062 --> 00:00:11,891
plus 2x plus 1

4
00:00:11,891 --> 00:00:15,293
and then they say find (f + g)(x)

5
00:00:15,293 --> 00:00:16,911
and this looks a little bit bizzare

6
00:00:16,911 --> 00:00:18,264
what kind of notation is this

7
00:00:18,264 --> 00:00:20,060
and that's really the core of this problem

8
00:00:20,060 --> 00:00:21,972
is just to realize that when someone writes

9
00:00:21,972 --> 00:00:24,988
(f +g) in parentheses of x

10
00:00:24,988 --> 00:00:33,441
is just notation for, this is the same thing as

11
00:00:33,441 --> 00:00:37,839
f(x) + g(x)

12
00:00:37,839 --> 00:00:42,089
you can view (f + g) as a new function

13
00:00:42,089 --> 00:00:44,039
that's created by adding the other twp function

14
00:00:44,039 --> 00:00:46,680
when you view it like this

15
00:00:46,680 --> 00:00:48,806
then you really just have to add these two functions

16
00:00:48,806 --> 00:00:52,605
so f(x) given the definition

17
00:00:52,605 --> 00:00:57,220
is 9 - x squared

18
00:00:57,220 --> 00:01:00,688
and g(x) given the defintition

19
00:01:00,688 --> 00:01:03,278
right over here

20
00:01:03,278 --> 00:01:07,829
'is 5 times x squared plus 2x plus 1

21
00:01:07,829 --> 00:01:10,045
so when you add f(x) to g(x)

22
00:01:10,045 --> 00:01:11,222
this is going to be equal to

23
00:01:11,222 --> 00:01:14,029
and I'm just re-writing this over here

24
00:01:14,029 --> 00:01:17,120
the f(x) part is 9 - x squared

25
00:01:17,120 --> 00:01:19,211
and then you have the plus

26
00:01:19,211 --> 00:01:21,323
in yellow

27
00:01:21,323 --> 00:01:23,575
plus the g(x) part

28
00:01:23,575 --> 00:01:25,788
which is 5 times x squared

29
00:01:25,788 --> 00:01:28,624
plus 2x plus 1

30
00:01:28,624 --> 00:01:30,794
and now we can simplify this a little bit

31
00:01:30,794 --> 00:01:34,645
let me just get rid of the parentheses

32
00:01:34,645 --> 00:01:37,113
so this is equal to

33
00:01:37,113 --> 00:01:40,410
9 minus x squared plus

34
00:01:40,410 --> 00:01:43,906
since this is positive we don't have to worry about the parenthese

35
00:01:43,906 --> 00:01:50,494
so plus 5 x squared plus 2x plus 1

36
00:01:50,494 --> 00:01:52,558
and then we have two x squared terms

37
00:01:52,558 --> 00:01:56,005
we have 5 x squared and then we have negative x squared

38
00:01:56,005 --> 00:01:59,644
so 5 x squared minus x sqaured is 4 x squared

39
00:01:59,644 --> 00:02:02,397
so you get 4 x squared when you combine these two terms

40
00:02:02,397 --> 00:02:04,861
and you only have one 1st degree term

41
00:02:04,861 --> 00:02:05,879
2x there

42
00:02:05,879 --> 00:02:07,661
so plus 2x

43
00:02:07,661 --> 00:02:10,411
and then you have two constant terms

44
00:02:10,411 --> 00:02:12,729
or zero degree terms

45
00:02:12,729 --> 00:02:14,680
you have the 9 and youhave the 1

46
00:02:14,680 --> 00:02:17,461
so 9 plus 1 gets us to ten

47
00:02:17,461 --> 00:02:19,026
so we're done

48
00:02:19,026 --> 00:02:21,776
(f + g)(x)

49
00:02:21,776 --> 00:02:23,228
is equal to

50
00:02:23,228 --> 00:02:25,722
4 x sqaured plus 2x plus 10

51
00:02:25,722 --> 00:02:27,565
notice this is a new function

52
00:02:27,565 --> 00:02:30,087
that is created by summing the function definitons