7. For each of the following, give an example of functions f: A → B and g: B C that satisfy the stated conditions, or explain why no such example exists. * (a) The function f is a surjection, but the function gof is not a surjection. * (b) The function f is an injection, but the function gof is not an injection. (c) The function g is a surjection, but the function g of is not a surjection. (d) The function g is an injection, but the function go ƒ is not an injection. (e) The function f is not a surjection, but the function gof is a surjection. * (f) The function f is not an injection, but the function gof is an injection. (g) The function g is not a surjection, but the function gof is a surjection. (h) The function g is not an injection, but the function gof is an injection.
7. For each of the following, give an example of functions f: A → B and g: B C that satisfy the stated conditions, or explain why no such example exists. * (a) The function f is a surjection, but the function gof is not a surjection. * (b) The function f is an injection, but the function gof is not an injection. (c) The function g is a surjection, but the function g of is not a surjection. (d) The function g is an injection, but the function go ƒ is not an injection. (e) The function f is not a surjection, but the function gof is a surjection. * (f) The function f is not an injection, but the function gof is an injection. (g) The function g is not a surjection, but the function gof is a surjection. (h) The function g is not an injection, but the function gof is an injection.
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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Transcribed Image Text:7. For each of the following, give an example of functions f: A → B and
g: B C that satisfy the stated conditions, or explain why no such example
exists.
* (a) The function f is a surjection, but the function gof is not a surjection.
* (b) The function f is an injection, but the function gof is not an injection.
(c) The function g is a surjection, but the function g of is not a surjection.
(d) The function g is an injection, but the function go ƒ is not an injection.
(e) The function f is not a surjection, but the function gof is a surjection.
* (f) The function f is not an injection, but the function gof is an injection.
(g) The function g is not a surjection, but the function gof is a surjection.
(h) The function g is not an injection, but the function gof is an injection.
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