0:03 hi guys it's me teacher going in today's
0:05 video we will talk about the composite
0:08 function or composition of function
0:10 so we have here this notation
0:12 this is read as f
0:15 circle of G of X or
0:19 F composite G of X and that is equal to
0:22 this notation f g of X we're in in this
0:25 function since the variable F or the
0:28 function f comes first before G
0:30 G will be the input or the input function
0:31 function
0:34 with respect to the function f so
0:37 without further Ado let's do this topic
0:43 we are given two different functions f
0:46 of x is equal to 3x minus 5 and the
0:50 other is 3x at 3 of x g of x
0:53 is equal to x squared plus two and right
1:00 evaluate this one we have f
1:04 of G of 2 and the other is G of f of
1:07 negative one let's start with number one
1:12 in this case RF of G of 2 here
1:16 first we will try to evaluate f
1:17 f
1:19 of G
1:21 of X that is the same as that
1:24 okay now what will happen here is that
1:27 in this case guys
1:29 we will move this one since
1:30 since
1:33 your function f
1:37 comes first before G
1:39 we will plug in
1:43 this x square plus 2
1:46 to replace the variable X in
1:50 3x minus five so it goes like this three
1:52 copy three
1:55 then your X this x will be replaced by x square
1:56 square
1:58 times x square
2:00 plus 2
2:12 that is f
2:15 look at this one your gfx is inside the
2:17 parenthesis this will be the input
2:19 so we will replace the variable x 3
2:21 times x square
2:23 plus 2 minus 5. so what will happen
2:34 is that we will replace this variable X
2:37 by 2 and it will become 3
2:41 times
2:43 2 square
2:49 plus 2 minus 5. so what will happen is
2:50 that you need to simplify this to become 3
2:52 3
2:55 times 2 squares four
2:59 plus two then we have minus five simplify
3:01 simplify three
3:02 three
3:04 times four plus two which is equal to six
3:06 six
3:08 and then minus 5.
3:12 so this is three times six is eighteen
3:15 minus five therefore
3:17 your f
3:19 of G
3:24 of 2 is equal to 15 minus 18 minus 5
3:27 which is equal to 13. guys don't be
3:28 confused about these two different
3:33 notations if the variable F comes first
3:36 meaning your input is
3:38 the function G
3:41 if the function G comes first
3:43 your function f will be the input okay
3:44 let's continue
3:47 here number two we have G of f of
3:48 negative one
3:50 so it will become G
3:51 G off
3:53 off f
3:54 f
4:03 we will use this and this 3x minus 5
4:05 will be replaced or we will be using
4:06 this to substitute for the value
4:10 variable X and it will become like this
4:13 x squared that is x squared by copy this one
4:14 one
4:17 3x minus 5 Square
4:18 Square
4:26 X squaring
4:29 now after doing that remember that you
4:32 are asked to evaluate negative one
4:34 we will replace this x by negative one
4:36 it will become 3
4:37 3
4:39 times negative one
4:43 minus 5 square plus two
4:46 so simplify that into three times
4:49 negative 1 is negative three
4:50 three
4:52 minus five
4:56 then square plus 2. so simplify that
4:59 until your negative three minus five is
5:01 negative eight Square
5:03 Square
5:06 plus 2 and negative 8
5:10 squared is not negative 64. right the
5:13 answer is 60 4 and then plus 2. therefore
5:14 therefore
5:25 of f
5:27 of negative 1
5:32 is equal to 64 plus 1 and that is 66.
5:34 and this is the answer guys
5:36 so I hope guys learned something from
5:40 this video on how to
5:42 evaluate composite functions so if
5:45 you're new to my channel don't forget to
5:46 like And subscribe button hit the Bell
5:48 button for you to be updated starting
5:53 latest uploads again it's me to turgon
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