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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