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Unformatted text preview: Work out each problem. Circle the letter that appears before your answer. 1. If f(x) = 2x x , then for which of the following values of x does f(x) = x ? (A) (B) (C) (D) (E) 2.
1 4 1 2 4. 2 4 8 If f(x) = x2 and g(x) = x + 3, then g(f(x)) = (A) x + 3 (B) x2 + 6 (C) x + 9 (D) x2 + 3 (E) x3 + 3x2 If f(x) = 2 , then f(x2) ÷ ( f ( x ) ) = (A) x3 (B) 1 (C) 2x2 (D) 2 (E) 2x
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2 5. If f(a) = a–3 – a–2 , then f ( 1 ) = 3 (A) (B) (C) (D) (E) –6
1 6 1 6 9 18 3. If f(x) = x2 + 3x – 4, then f(2 + a) = (A) a2 + 7a + 6 (B) 2a2 – 7a – 12 (C) a2 + 12a + 3 (D) 6a2 + 3a + 7 (E) a2 – a + 6 www.petersons.com Numbers and Operations, Algebra, and Functions 255 6. FUNCTIONS—DOMAIN AND RANGE
A function consists of a rule along with two sets—called the domain and the range. The domain of a function f(x) is the set of all values of x on which the function f(x) is defined, while the range of f(x) is the set of all values that result by applying the rule to all values in the domain. By definition, a function must assign exactly one member of the range to each member of the domain, and must assign at least one member of the domain to each member of the range. Depending on the function’s rule and its domain, the domain and range might each consist of a finite number of values; or either the domain or range (or both) might consist of an infinite number of values. Example: In the function f(x) = x + 1, if the domain of x is the set {2,4,6}, then applying the rule that f(x) = x + 1 to all values in the domain yields the function’s range: the set {3,5,7}. (All values other than 2, 4, and 6 are outside the domain of x, while all values other than 3, 5, and 7 are outside the function’s range.) Example: In the function f(x) = x2, if the domain of x is the set of all real numbers, then applying the rule that f(x) = x2 to all values in the domain yields the function’s range: the set of all nonnegative real numbers. (Any negative number would be outside the function’s range.) Exercise 6
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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
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