For each of the following mappings indicate what type of function they are (if any). Use the following key: i. Not a function ii. A function which is neither onto nor one-to-one iii. A function which is onto but not one-to-one iv. A function which is one-to-one but not onto A function which is both onto and one-to-one V. Clearly indicate in the text box below which choice you've made from the options above for each of the parts below. (a) mapping f from Z to N defined by f(n)= |2n|. (b) mapping f from {1, 3} to {2, 4} defined by f(n) = 2n. (c) The mappingffrom R to R defined by f(n)= 8–2n. (d) The mapping ƒ from R to Z defined by f(x) = [x+1] (e) The mappingf from R+ to R+ defined by f(x) =x – 1.
For each of the following mappings indicate what type of function they are (if any). Use the following key: i. Not a function ii. A function which is neither onto nor one-to-one iii. A function which is onto but not one-to-one iv. A function which is one-to-one but not onto A function which is both onto and one-to-one V. Clearly indicate in the text box below which choice you've made from the options above for each of the parts below. (a) mapping f from Z to N defined by f(n)= |2n|. (b) mapping f from {1, 3} to {2, 4} defined by f(n) = 2n. (c) The mappingffrom R to R defined by f(n)= 8–2n. (d) The mapping ƒ from R to Z defined by f(x) = [x+1] (e) The mappingf from R+ to R+ defined by f(x) =x – 1.
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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giving reasons
![For each of the following mappings indicate what type of function they are
(if any). Use the following key:
i.
Not a function
ii.
A function which is neither onto nor one-to-one
iii.
A function which is onto but not one-to-one
iv.
A function which is one-to-one but not onto
A function which is both onto and one-to-one
V.
Clearly indicate in the text box below which choice you've made from the
options above for each of the parts below.
(a) mapping f from Z to N defined by f(n)= |2n|.
(b) mapping f from {1, 3} to {2, 4} defined by f(n) = 2n.
(c) The mappingffrom R to R defined by f(n)= 8–2n.
(d) The mapping ƒ from R to Z defined by f(x) = [x+1]
(e) The mappingf from R+ to R+ defined by f(x) =x – 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa55bbc8f-555c-4f40-91f5-c2abe3b5298b%2F91def52b-8410-4089-8a83-378d35e2e203%2F9f0wkrs_processed.png&w=3840&q=75)
Transcribed Image Text:For each of the following mappings indicate what type of function they are
(if any). Use the following key:
i.
Not a function
ii.
A function which is neither onto nor one-to-one
iii.
A function which is onto but not one-to-one
iv.
A function which is one-to-one but not onto
A function which is both onto and one-to-one
V.
Clearly indicate in the text box below which choice you've made from the
options above for each of the parts below.
(a) mapping f from Z to N defined by f(n)= |2n|.
(b) mapping f from {1, 3} to {2, 4} defined by f(n) = 2n.
(c) The mappingffrom R to R defined by f(n)= 8–2n.
(d) The mapping ƒ from R to Z defined by f(x) = [x+1]
(e) The mappingf from R+ to R+ defined by f(x) =x – 1.
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