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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 $f : R \to R$ and let $f (x) > 0$ for all $x \in R$ . Show that f(x) is strictly decreasing if and only if the functionrole="math" localid="1668414965156" $g (x) = 1 / f (x)$ is strictly increasing.

Show that the function $f (x) = |x|$ from the set of real numbers to the set of non-negative real numbers is not invertible, but if the domain is restricted to the set of non- negative real numbers, the resulting function is invertible.

Compute each of these double sums

\begin{aligned} \sum_{i = 1}^{2} \sum_{j = 1}^{3} (i + j) \\ \sum_{i = 0}^{2} \sum_{j = 0}^{3} (2 i + 3 j) \\ \sum_{i = 1}^{3} \sum_{j = 0}^{2} i \\ \sum_{i = 0}^{2} \sum_{j = 1}^{3} ij \end{aligned}

Question: Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a teacher his or her

Office
Assigned bus to chaperone in a group of buses taking students on a field trip
Salary
Social security number

Construct a truth table for each of these compound propositions.

a. $p \to \neg q$

b. $\neg p \leftrightarrow q$

c. $(p \to q) \lor (\neg p \to q)$

d. $(p \to q) \land (\neg p \to q)$

e. localid="1663757061530" $(p \leftrightarrow q) \lor (\neg p \leftrightarrow q)$

f. $(p \leftrightarrow q) \lor (\neg p \leftrightarrow q)$

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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

Step by step solution

Step: 1

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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

Decision Maths

Calculus

Pure Maths

Theoretical and Mathematical Physics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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