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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 2: Q23E (page 153)

Determine whether each of these functions is a bijection from R to R.
$f (x) = 2 x + 1$
$f (x) = x^{2} + 1$
$f (x) = x$
$f (x) = (x^{2} + 1) / (x^{2} + 2)$

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Most popular questions from this chapter

Let $S = {- 1, 0, 2, 4.7}$ . Find f(S) if

role="math" localid="1668419106110" $f (x) = 1$
role="math" localid="1668419096298" $f (x) = 2 + 1$
role="math" localid="1668419089300" $f (x) = [x / 5]$
$f (x) = [(x^{2} + 1) / 3]$

Question: Let $f : R \to R$ and $f (x) > 0$ let for all $x \in R$ . Show that f(x) is strictly increasing if and only if the function $g (x) = 1 / f (x)$ is strictly decreasing.

Show that the function $f (x) = e^{x}$ from the set of real numbers to the set of real numbers is not invertible, but if the co domain is restricted to the set of positive real numbers, the resulting function is invertible.

Prove or disprove each of these statements about the floor and ceiling functions.

$[⌊ x ⌋ ⌉ = ⌊ x ⌋$ for all real numbers x.
$⌊ 2 x ⌋ = 2 ⌊ x ⌋$ whenever x is a real number.
$⌈ x ⌉ + ⌈ y ⌉ - ⌈ x + y ⌉ = 0 or 1$ whenever x and y are real numbers.
$⌈ x y ⌉ = ⌈ x ⌉ ⌈ y ⌉$ for all real numbers x and y.
$⌈\frac{x}{2}⌉ = ⌊\frac{x + 1}{2}⌋$ for all real numbers x.

conjecture a formula for the terms of the sequence that begins $8, 14, 32, 86, 248$ and find the next three terms of your sequence.

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Determine whether each of these functions is a bijection from R to R.
$f (x) = 2 x + 1$
$f (x) = x^{2} + 1$
$f (x) = x$
$f (x) = (x^{2} + 1) / (x^{2} + 2)$

Short Answer

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Step: 1

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Most popular questions from this chapter

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Determine whether each of these functions is a bijection from R to R. fx=2x+1fx=x2+1fx=xfx=x2+1/x2+2

Short Answer

Step by step solution

Step: 1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Probability and Statistics

Applied Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Determine whether each of these functions is a bijection from R to R.
$f (x) = 2 x + 1$
$f (x) = x^{2} + 1$
$f (x) = x$
$f (x) = (x^{2} + 1) / (x^{2} + 2)$