SAT Math Part 12 - Evaluating Composite Functions - Free Educational videos for Students in K-12 | Lumos Learning

SAT Math Part 12 - Evaluating Composite Functions - Free Educational videos for Students in k-12


SAT Math Part 12 - Evaluating Composite Functions - By The Organic Chemistry Tutor



Transcript
00:00 number 41 . If f of X is equal two
00:05 , x squared plus two reacts -8 and G of
00:09 X is equal to the absolute value of seven minus
00:13 X plus three . Then what is the value of
00:18 G of F . F 3 ? So what we
00:22 need to do here is we need to evaluate a
00:24 composite function . We have a function inside of another
00:29 function . So first let's calculate the value of the
00:34 stuff inside f . of three . So we just
00:37 gotta plug in three into that expression . So it's
00:42 gonna be three squared plus three times 3 -8 .
00:47 Three squared is 93 times streets . Also nine Now
00:52 9 -8 is one . So we have 9-plus 1
00:56 which is 10 . Yeah , Thus f of three
00:59 is equal to 10 . So going back to that
01:04 expression , we have G of f of three Now
01:08 because FF three is equal to 10 , we can
01:10 replace it with him . So now what we need
01:13 to do is Evaluate G when X is 10 .
01:18 So this is going to be the absolute value Of
01:21 7 -10 plus tree . Now 7 -10 is -3
01:28 . The absolute value of -3 is positive three .
01:32 So this becomes 3-plus 3 which is six . And
01:37 so we could say that G of F of three
01:39 is 6 . So C . Is the right answer
01:44 . 42 . If f of three is negative seven
01:49 and GF seven is 6 and F of negative seven
01:53 is negative four And G of -4 is five .
01:58 Then what is the value of G of F of
02:02 F . Of three ? So let's start by right
02:09 in this function . Yeah . So first let's evaluate
02:15 F of three . We're told that F of three
02:17 is negative seven . So let's replace what we have
02:20 here with -7 . So this becomes G of F
02:27 of negative seven . Now we know that f of
02:30 negative seven is negative four . So this becomes G
02:36 of 94 . And we can see that she of
02:38 -4 is five . And so this right here is
02:42 the answer . So as you can see , it's
02:44 not very difficult to evaluate a composite function even if
02:50 we have three functions involved . But B is the
02:55 correct answer for this problem . 43 . Using the
03:00 table shown below What is the value of G of
03:04 F . of -2 . So go ahead and try
03:08 this problem . As always . We're going to start
03:13 with the part on the inside . So what is
03:16 F of -2 . So using a table , we
03:22 need to use the second column which deals with F
03:24 of X . And we need to highlight the role
03:27 wear acts as -2 . So we can see that
03:30 F of negative two is going to be this value
03:33 for so G of F of negative two is equivalent
03:41 to G four Since F of -2 is equal to
03:46 four . Now what is GF 4 ? So using
03:50 the last column And the real where access four ,
03:53 we see that G of four is 7 . So
03:57 this is the final answer for this problem . Answer
04:00 choice E is the correct answer . 44 . If
04:06 F of X is equal to X square plus five
04:10 and G of axes to ex monastery , then ,
04:14 which of the following expressions is equivalent to F of
04:18 G FX to find F of G of X .
04:22 What we need to do is take G and insert
04:25 it into F . So f of axes x squared
04:30 plus five to write an expression of F of G
04:37 of X . We can replace G Fx with what
04:42 it's equal to . So G of X is two
04:45 X . Monastery . So everywhere we see an X
04:49 . We're gonna replace it with two X . Monastery
04:52 . So this would be x square plus five .
04:55 But instead of having X we're going to have to
04:58 X ministry inside it . So notice that it's squared
05:05 , which means that we have two of them multiply
05:08 to each other . So let's multiply these two by
05:12 no meals . two x times two X is going
05:15 to be four X squared and then we have two
05:19 X times negative three , Which is the same as
05:22 -3 times two acts And then -3 times negative three
05:27 . That's plus nine . Now we can combine these
05:32 two terms that's gonna be negative 12 x And nine
05:37 plus 5 is 14 . So the answer is four
05:41 X squared minus 12 X plus 14 , which is
05:45 answer choice B .
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SAT Math Part 12 - Evaluating Composite Functions is a free educational video by The Organic Chemistry Tutor.

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