An arco book arco is a registered trademark of Thomson Learning, Inc., and is used herein under license by Peterson’s. About The Thomson Corporation and Peterson’s

21. The correct answer is (D). g(7) means substitute 7 for x in the expression g(x) = 3 – x
2
g(7) = 3 – (7)
2
= –46
f(g(7)) = f(–46) which means substitute –46 for x in the expression f(x) = –x
2
– 3
f(–46) = (–46)
2
– 3 = –2119
f(f(g(7))) = f(f(–46)) = f(–2119) which means substitute –2119 for x in the expression f(x) = –x
2
– 3
f(–2119) = – (–2119)
2
– 3 = –4490164
22. The correct answer is (A). The rectangle with four equal sides is the square. And a square with
perimeter P will have sides of P/4. The area of this figure is:
You can also solve this problem by assuming a value for P. For example, let the perimeter of square
P be 4. On that assumption, each side has a length of 1, and the area of the square is 1. Now, substitute
4 for P in the answer choices until you find one that generates the value 1:
(A)
Correct!
(B)
Wrong!
(C)
4
2
= 16
Wrong!
(D)
2(4)
2
= 32
Wrong!
(E)
4(4)
2
= 64
Wrong!

---

Mathematics Level IC/IIC Subject Tests
213
ARCO
■ SAT II Subject Tests
w w w . p e t e r s o n s . c o m / a r c o
23. The correct answer is (A). The defining characteristic of a function is “for each element in the
domain, there is only one element in the range.” Since the x coordinates are the domain, and the y
coordinates are the range, for each x coordinate there can be no more than one y coordinate. The
graphs of (B), (C), (D), and (E) all fit this description. (A) does not. For the relationship described by
(A), every value of x (except for one) has two y values.