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3. Determine whether each of the following functions is a bijection and explain why. (a) f: R R, defined as f(r) = 2r. %3D (b) f: N N, defined as f(r) = 2x. %3D (c) f: N N, defined as f(x) = [x/2]. %3D

3. Determine whether each of the following functions is a bijection and explain why. (a) f: R R, defined as f(r) = 2r. %3D (b) f: N N, defined as f(r) = 2x. %3D (c) f: N N, defined as f(x) = [x/2]. %3D

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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3. Determine whether each of the following functions is a bijection and explain why. (a) \( f : \mathbb{R} \to \mathbb{R}, \) defined as \( f(x) = 2x. \) (b) \( f : \mathbb{N} \to \mathbb{N}, \) defined as \( f(x) = 2x. \) (c) \( f : \mathbb{N} \to \mathbb{N}, \) defined as \( f(x) = \lfloor x/2 \rfloor. \) (d) \( f : \mathbb{R} \to \mathbb{R}, \) defined as \( f(x) = x^2 + 1. \) (e) \( f : \mathbb{R} \to \mathbb{R}, \) defined as \( f(x) = (5x - 2)/3. \)
Transcribed Image Text:3. Determine whether each of the following functions is a bijection and explain why. (a) \( f : \mathbb{R} \to \mathbb{R}, \) defined as \( f(x) = 2x. \) (b) \( f : \mathbb{N} \to \mathbb{N}, \) defined as \( f(x) = 2x. \) (c) \( f : \mathbb{N} \to \mathbb{N}, \) defined as \( f(x) = \lfloor x/2 \rfloor. \) (d) \( f : \mathbb{R} \to \mathbb{R}, \) defined as \( f(x) = x^2 + 1. \) (e) \( f : \mathbb{R} \to \mathbb{R}, \) defined as \( f(x) = (5x - 2)/3. \)
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Bijection function:

 If a function f: A → B satisfies both the one-to-one function and onto function

 

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