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Exercise 5.96. Give an example of each of the following and give an informal proof of the properties you claim. (a) A function f : R → R that is one-to-one but not onto. (b) A function ƒ : R → R that is onto but not one-to-one.

Exercise 5.96. Give an example of each of the following and give an informal proof of the properties you claim. (a) A function f : R → R that is one-to-one but not onto. (b) A function ƒ : R → R that is onto but not one-to-one.

Advanced Engineering Mathematics
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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**Exercise 5.96.** Give an example of each of the following and give an informal proof of the properties you claim. (a) A function \( f : \mathbb{R} \to \mathbb{R} \) that is one-to-one but not onto. (b) A function \( f : \mathbb{R} \to \mathbb{R} \) that is onto but not one-to-one.
Transcribed Image Text:**Exercise 5.96.** Give an example of each of the following and give an informal proof of the properties you claim. (a) A function \( f : \mathbb{R} \to \mathbb{R} \) that is one-to-one but not onto. (b) A function \( f : \mathbb{R} \to \mathbb{R} \) that is onto but not one-to-one.
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