1. Let X = {m, a, t, h}, Y = {1,4, 0}, Z = {d,i, s, c, r, e,t, e} (a) Define a function f : X →Y that is onto, but not one-to-one. (b) Define a function g : X → Z that is one-to-one, but not onto. (c) Define a function h : X → X that is neither one-to-one nor onto.

1. Let X = {m, a, t, h}, Y = {1,4, 0}, Z = {d,i, s, c, r, e,t, e} (a) Define a function f : X →Y that is onto, but not one-to-one. (b) Define a function g : X → Z that is one-to-one, but not onto. (c) Define a function h : X → X that is neither one-to-one nor onto.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

1. Let X = {m, a, t, h}, Y = {1,4, 0}, Z = {d, i, s, c, r, e, t, e}
(a) Define a function f : X → Y that is onto, but not one-to-one.
(b) Define a function g : X → Z that is one-to-one, but not onto.
(c) Define a function h : X → X that is neither one-to-one nor onto.
(d) Define a function k : X → X that is bijective but is not the identity function on X.

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