2. Let W = {5,6, 7}, X = {1,2,3, 4}, Y = {C, D, E}, and Z = {a, 3, 7} (a) Can there be a function f: Z - W that is one-to-one, but not onto? If so, draw the arrow diagrams for such a function. If no such function exists, explain why. (b) Draw the arrow diagrams for a function g : Y → X that is neither one-to-one nor onto. (c) For a set S, the identity function is a function h : S -+ S where Vt E S, h(t) = t. Find a function f : X X that is one-to-one and onto, but not the identity function.

2. Let W = {5,6, 7}, X = {1,2,3, 4}, Y = {C, D, E}, and Z = {a, 3, 7} (a) Can there be a function f: Z - W that is one-to-one, but not onto? If so, draw the arrow diagrams for such a function. If no such function exists, explain why. (b) Draw the arrow diagrams for a function g : Y → X that is neither one-to-one nor onto. (c) For a set S, the identity function is a function h : S -+ S where Vt E S, h(t) = t. Find a function f : X X that is one-to-one and onto, but not the identity function.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.1: Functions

Problem 5E: A Function f is a rule that assigns to each element x in a set A exactly ________ element(s) called...

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