1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Goshia [24]
3 years ago
14

Let O be the set of even integers. Define f : Z ? O by f(n) = 2n. Prove that f is a bijection in the following two different way

s.
(a) Prove that f is both injective and surjective.

(b) Find an inverse g : O ? Z of f. (Show that g is an inverse of f.)
Mathematics
1 answer:
AysviL [449]3 years ago
7 0

Answer:

Check.

Step-by-step explanation:

a. Let f: \mathbb{Z} \rightarrow O such that f(n) = 2n.

Injective:

Let n, m \in \mathbb{Z} such that f(n)=f(m). Then,

2n = 2m and dividing both sides by 2 we obtain that n=m. Then f is injective.

Surjective:

Let n  \in O, so n = 2k for some integer k. Then, f(k) = n and therefore f is surjective.

b. Let  g: O \rightarrow \mathbb{Z} such that g(n) = n/2. Then,

g(f(n)) = g(2n) = 2n/2 = n, and for m \in O

f(g(m)) = f(m/2) = 2*m/2 = m.

Therefore, g is the inverse of f.

You might be interested in
PLEASE ANSWER ASASP WITH WORK FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!
Andru [333]

Answer:

B

Step-by-step explanation:

Class and cost per class should be multipled so must be A or B. The amount of money she has should be greater than or equal to her costs or she can't afford it! So B.

3 0
3 years ago
Read 2 more answers
2.
zavuch27 [327]
A. For y= 2x-1, the slope is 2 and the y intercept is -1. Therefore, we should first plot (0,-1). From there, for each increment of x, increase y by 2. For y= 4x-5, the slope is 4 and the y ntercelt is -5. Therefore we should plot (0,-5) and plot an increase of 4 on the y axis per increase of 1 on the x axis. The solution is where the lines cross.

B. (2,3)
8 0
3 years ago
6 family members share 1/4 of a of chocolate fudge what fraction of a pound does each family member get if they share equally .
photoshop1234 [79]

Answer:

The answer is 1/10

Step-by-step explanation:

7 0
2 years ago
A spinner is divided into two equal parts, one red and one blue. The set of possible outcomes when the spinner is spun twice is
Hunter-Best [27]

A 2-column table that has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0. 25, 0. 5, 0. 25.

<h3>What is Probability?</h3>

The probability helps us to know the chances of an event occurring.

\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

We know about the probability, therefore, let's find the probability of each of the cases.

When the number of success of the spinner landing on blue is none, therefore, the spinner does not land on the blue color at all.

\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

Now, as it is given that there is only one case when the spinner does not land on the blue side(RR) in the set, S = {RR, RB, BR, BB}. therefore,

\rm{Probability(X=0)=\dfrac{1}{4} = 0.25

When the number of success of the spinner landing on blue is just once, therefore, the spinner does land on the blue color only once out of the two spin.

\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

Now, as it is given that there are two cases when the spinner does land on the blue side(RB, BR) in the set, S = {RR, RB, BR, BB}. therefore,

\rm{Probability(X=1)=\dfrac{2}{4} = 0.25

When the number of success of the spinner landing on blue is twice, therefore, the spinner does land on the blue color both the times the spinner is spun.

\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

Now, as it is given that there is only one case when the spinner does land on the blue side twice(BB) in the set, S = {RR, RB, BR, BB}. therefore,

\rm{Probability=\dfrac{1}{4} = 0.25

Now, if we draw the table of the data and the probability we will get the following table,

x             P(X)

0           0.25

1            0.50

2           0.25

Hence, the table that is correct is table A, which is  A 2-column table that has 3 rows. The first column is labeled x with entries 0, 1, 2. The second column is labeled P x (x) with entries 0. 25, 0. 5, 0. 25.

Learn more about Probability:

brainly.com/question/795909

8 0
2 years ago
Does anyone know where he got the 32pie from?
Tems11 [23]
That might be the diameter of the circle
3 0
2 years ago
Other questions:
  • Hi can someone check my answers please
    15·1 answer
  • on a test, a student answered 12 questions correctly. this number represents 80% of the total number of questions were on the te
    14·1 answer
  • Multiply each polynomial <br> (x - 7)(x - 4)
    6·1 answer
  • A boat and trailer together weigh 2265 pounds. How much force is required to hold the boat and trailer on an 18° incline to the
    11·1 answer
  • In 2003, the Accreditation Council for Graduate Medical Education (ACGME) implemented new rules limiting work hours for all resi
    9·1 answer
  • a baseball is thrown a distance of 20 meters . what is its speed if it takes 0.5 seconds to cover the distance?
    10·2 answers
  • G(x) to g(x)=-[x]+3 what is the domain of g(x)?
    14·1 answer
  • the area of a Trapezium is 132 cm². Its height is 14 cm the larger parallel side is longer than the other by 16 cm. find the len
    11·1 answer
  • SOMEONE HELP PLEASE EASY MATHHH PERCENTAGE OF AN AMOUNT
    7·1 answer
  • Please help asap
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!