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Jx + 1 if x is even b. f(x) = S = {0, 1, 5, 9}, T = Z – E if x is odd; 2 7 11

Jx + 1 if x is even b. f(x) = S = {0, 1, 5, 9}, T = Z – E if x is odd; 2 7 11

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3b. only please
1. For the given sets, form the indicated Cartesian product. a. A × B; A = {a, b}, B = {0, 1} b. B X A; A = {a; b}, B = {0, 1} c. A X B; A = {2, 4, 6, 8}, B = {2} d. B X A; A = {1, 5, 9}, B = {-1, 1} e. BX A; A = B = {1, 2, 3} 2. For each of the following mappings, state the domain, the codomain, and the range, where f: E →Z. a. f(x) = x/2, x E E b. f(x) = x, x E E c. f(x) = |x|, x E E d. f(x) = x + 1, x E E (3. For each of the following mappings, write out f(S) and f'(T) for the given S and T, where f: Z →Z. a. f(x) = |x|; S = Z – E, T = {1, 3, 4} Sx + 1 if x is even b. f(x) = S = {0, 1, 5, 9}, T = Z – E if x is odd; Co f(x) = x²; S ={-2, – 1, 0, 1, 2}, T = {2,7, 11} d. f(x) = |x| – x; S = T = {-7, -1,0, 2, 4} 4. For each of the following mappings f: Z→Z, determine whether the mapping is onto and whether it is one-to-one. Justify all negative answers. a. f(x) = 2x b. f(x) = 3x C f(x) = x + 3 e. f(x) = |x| d. f(x) = x f. f(x) = x – |x| %3D е.
Transcribed Image Text:1. For the given sets, form the indicated Cartesian product. a. A × B; A = {a, b}, B = {0, 1} b. B X A; A = {a; b}, B = {0, 1} c. A X B; A = {2, 4, 6, 8}, B = {2} d. B X A; A = {1, 5, 9}, B = {-1, 1} e. BX A; A = B = {1, 2, 3} 2. For each of the following mappings, state the domain, the codomain, and the range, where f: E →Z. a. f(x) = x/2, x E E b. f(x) = x, x E E c. f(x) = |x|, x E E d. f(x) = x + 1, x E E (3. For each of the following mappings, write out f(S) and f'(T) for the given S and T, where f: Z →Z. a. f(x) = |x|; S = Z – E, T = {1, 3, 4} Sx + 1 if x is even b. f(x) = S = {0, 1, 5, 9}, T = Z – E if x is odd; Co f(x) = x²; S ={-2, – 1, 0, 1, 2}, T = {2,7, 11} d. f(x) = |x| – x; S = T = {-7, -1,0, 2, 4} 4. For each of the following mappings f: Z→Z, determine whether the mapping is onto and whether it is one-to-one. Justify all negative answers. a. f(x) = 2x b. f(x) = 3x C f(x) = x + 3 e. f(x) = |x| d. f(x) = x f. f(x) = x – |x| %3D е.
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The given function isfx=x+1if x is evenxif x is oddS=0, 1, 5, 9T=ℤ-Ewhere ℤ is the set of integers and E is the set of even integers

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