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Unformatted text preview: e x + 1 to 3, 8, and 15:
(3) + 1 = 4 = +2 (8) + 1 = 9 = +3 (15) + 1 = 16 = +4 ( ) ( ) ( ) ( )( )
1 4 =2 1 4 1 4 = 1 2 1 2 = 1 4 Another way to solve the problem is to let x = 2 x x , then solve for x by squaring both sides of the equation (look for a root that matches one of the answer choices):
x = 2x x 1= 2 x 1 =x 2 1 =x 4 Choice (B) provides the members of the range. Remember that x means the positive square root of x. 2. (E) To determine the function’s range, apply the rule (6a – 4) to –6 and to 4. The range consists of all real numbers between the two results: 6(–6) – 4 = –40 6(4) – 4 = 20 The range of the function can be expressed as the set R = {b  –40 < b < 20}. Of the five answer choices, only (E) does not fall within the range. 3. (D) The function’s range contains only one member: the number 0 (zero). Accordingly, to find the domain of x, let f(x) = 0, and solve for all possible roots of x:
x 2 − 2x − 3 = 0 ( x − 3)( x + 1) = 0 x − 3 = 0, x + 1 = 0 x = 3, x = −1 2. (E) First, note that any term raised to a negative power is equal to 1 divided by the term to the absolute value of the power. Hence:
a −3 − a −2 = 1 1 − a3 a 2 Using this form of the function, substitute 3 for a , then simplify and combine terms:
f 1 ( )=
1 3 () ()
1 3 3 1 3 1 − 1 2 = 1
1 27 − 1
1 9 = 27 − 9 = 18 3. (A) In the function, substitute (2 + a) for x. Since each of the answer choices indicates a quadratic expression, apply the distributive property of arithmetic, then combine terms:
f (2 + a) = (2 + a)2 + 3(2 + a) − 4 = (2 + a)(2 + a) + 6 + 3a − 4 = 4 + 4 a + a 2 + 6 + 3a − 4 = a 2 + 7a + 6 Given that f(x) = 0, the largest possible domain of x is the set {3, –1}. 4. (B) The question asks you to recognize the set of values outside the domain of x. To do so, first factor the trinomial within the radical into two binomials:
f ( x ) = x 2 − 5 x + 6 = ( x − 3)( x − 2) 4. (D) Substitute f(x) for x in the function g(x) = x + 3: g(f(x)) = f(x)...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at EmbryRiddle FL/AZ.
 Spring '10
 Colon
 SAT

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