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
I’ll give you brainless please help me
Papessa [141]

Answer:

I'm pretty sure its 4

6 0
2 years ago
PLZ HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!During a 4-month-long drought, the water level in a lake changed
Dafna1 [17]

Answer:

-78

Step-by-step explanation:

4 Months is -312 so dividing by 4 will give the decrease of one month:

-312 ÷ 4 = -78

3 0
3 years ago
Simplify completely the quantity 4 times x to the third power plus 5 times x to the 2nd power plus 3 times x all over x. (2 poin
ikadub [295]

Answer:   4x² + 5x + 3

<u>Step-by-step explanation:</u>

\dfrac{4x^3+5x^2+3x}{x}\\\\\\=\dfrac{x(4x^2+5x+3)}{x}\qquad \text{factored out the common term from the numerator}\\\\\\=4x^2+5x+3\qquad \text{canceled out x from numerator and denominator}

8 0
3 years ago
I really need help pleaseeee
raketka [301]
12.92 I hope this helps
4 0
2 years ago
HELP HELP HELP HELP HELP HELP PLEASE I BEG U
kari74 [83]

Answer:

-3.2

Step-by-step explanation:

Do you have to work this out on paper because I just used a calculator but just add 3.1 + -6.3.

5 0
3 years ago
Other questions:
  • - 2 root 2 + root 2 ?
    15·1 answer
  • Can you guys please help?????????
    7·1 answer
  • If the balance of supplies at the start of the month was $900 and at the end of the month there was $450 on hand, the adjustment
    7·2 answers
  • What is the area of this figure
    11·1 answer
  • Last one and the bottom answer choice is <br> Y=(x-4)^2+1 <br> Thank you guys!
    11·1 answer
  • Can a composite number have more than one prime factorization
    5·1 answer
  • Point A is at -7, -3. There are 12 points between A and B. What are possible coordinates for point B?
    6·1 answer
  • Please help I never understood this a lot,
    12·1 answer
  • Select the decimal that is equivalent to the fraction 57 over 100
    8·1 answer
  • Determine whether or not the lines are parallel based on the
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!