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5. Give an example of: 1. A function f: N→ N that is injective but not surjective. 2. A function f: N→ N that is surjective but not injective. 3. A function f : R → R that is bijective. 4. A relation that is not a function.

5. Give an example of: 1. A function f: N→ N that is injective but not surjective. 2. A function f: N→ N that is surjective but not injective. 3. A function f : R → R that is bijective. 4. A relation that is not a function.

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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5. Give an example of: 1. A function \( f : \mathbb{N} \to \mathbb{N} \) that is injective but not surjective. 2. A function \( f : \mathbb{N} \to \mathbb{N} \) that is surjective but not injective. 3. A function \( f : \mathbb{R} \to \mathbb{R} \) that is bijective. 4. A relation that is not a function.
Transcribed Image Text:5. Give an example of: 1. A function \( f : \mathbb{N} \to \mathbb{N} \) that is injective but not surjective. 2. A function \( f : \mathbb{N} \to \mathbb{N} \) that is surjective but not injective. 3. A function \( f : \mathbb{R} \to \mathbb{R} \) that is bijective. 4. A relation that is not a function.
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