Explanation for Question 24 From the Math (Calc) Section on the Official Sat Practice Test 9
Question 24 reads if F of X equals five X squared, 2 minus three and F of X plus a equals five X squared plus 30 3 X plus 42. What is the value of a? 4 So the thing to note here is that this is saying that the function 5 that we're given is five X squared, 6 minus three. When you take that same function and plug X plus 7 a into it, you get this expression. 8 So let's do just that and figure out what AA is got. 9 F of X equals five X squared, 10 minus three, and F of X plus a is 11 equal to five. And then just in the X place, 12 we plug in X plus a squared minus three, 13 and then we can simplify that out and get five 14 X plus a times X plus a minus three, 15 we got X squared plus a 16 X plus X plus a squared. 17 And then that whole thing will be multiplied by five minus 18 three. So we're left with five X squared plus 19 X plus X is two AIX. 20 And then times five is 10, a X plus five, 21 a squared minus three. 22 Okay. So looking at this, 23 this is equal to five of X plus a, 24 and we want that to be equal to we are, 25 we also know that five F of X plus a is equal to five 26 X squared plus 30 X plus 42. So five X squared plus 30 27 X plus 42 is equal to five X squared 28 plus 10 X plus five, 29 a squared minus 32. So this term matches up with this 30 term and this term matches up with this term and we can solve from 31 there. So 30 X has got to be equal to 10, 32 eight X. So divide both sides by X we're left with 30 is equal 33 to 10 and then dividing both sides by 10. 34 We get that a is equal to three and that's how we get answer 35 choice C.
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