Concept explainers
A function
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Linear Algebra with Applications (2-Download)
- D: Remind that the set F of all functions from R to R is a vector space. 2. Prove that for any function f the function e(x) = f(x)+ƒ(−ª) is even and the function o(x) 2 is odd. What is their sum? f(x)-f(-x) 2arrow_forward3. Let f(x) = x² + 3 and g(x) and [3, 0), respectively. = Vx – 3 be functions defined on [0, 0) i. Draw the graphs of f and g on the same plane with the equation y = x. (Use different colors for each graph, if possible, and label the graphs properly.) ii. Give an argument about the relationship of the functions f and g. (Write it in paragraph form with at least 2 sentences.)arrow_forwardLet A = {1,2,3}, B B = Define the functions f: A→ C and g: B → C by f(1) = 7, f(2)= 9, f(3) = 7, Does there exist a function h: A B such that go h = f? Does there exist a function k: B→ A such that fok = g? Justify your answers. = {4,5,6}, {4,5,6}, C = {7, 8, 9, 10}. g(4) = 10, g(5) = 7, g(6) = 9.arrow_forward
- Let A = {1,2,3}, Define the functions f: A → C and g: B → C by f(1) = 7, f(2) = 9, f(3) = 7, g(4) = 10, Does there exist a function h: A → B such that goh = f? Does there exist a function k: B → A such that fo k = g? Justify your answers. B = {4,5,6}, C = {7, 8, 9, 10}. g(5) = 7, g(6) = 9.arrow_forwardGiven that A = {1, 2, 3, 4, 5} and B = {x, y, z}, determine which of the sets of ordered pairs represents a function from A to B. Explain the reason(s) why or why not for each i) {(1, z), (2, x), (3, y), (2, x)} ii) {(1, z), (3, y), (2, x), (4, x), (5, 5)} iii) {(1, y), (2, y), (5, x), (3, y), (4, y)} Which of the following graphs represent y as a functionof x? Explain the reason(s) why or why not for each ii)arrow_forwardLet f be the function from {a, b, c, d, e} to {1,2,3,4} with ƒ(a) = 3, ƒ (b) = 1, ƒ(c) = 2, ƒ(d) = 4 and ƒ(e) = 2. a. Is the function f one-to-one? Justify your answer.arrow_forward
- Let X = {h, p, t, v, w}, and Y = {4,7, 10, 12, 15, 16, 21, 24, 29, 30}. f = {(h, 21), (p, 29), (t, 24), (v, 24), (w, 10)} defines a function from X to Y. X is the of the function, and Y is the of the function.arrow_forwardplease help me with letters (b) and (d). thanksarrow_forwardWrite it in detail please.arrow_forward
- Given u=(u1, u2) and v=(v1, v2), then function = u1 v1 - 2 u2 v2 is : Select one: a. a valid inner-product function b. satisfying is always positive C. a commutative function d. not a valid inner-product functionarrow_forwardGiven g = {(1, c),(2, a),(3, d)}, a function from X = {1, 2, 3} to Y = {a, b, c, d}, and f = {(a, γ),(b, α),(c, δ),(d, γ)}, a function from Y to Z = {α, β, γ, δ}, write f ◦ g as a set of ordered pairs.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell