Mathematics College

From the given functions from Z x Z to Z, identify the onto functions. (Check all that apply.) Check All That Apply
a. f(m, n) = 2m-n b. f(m, n) = m 2-n2 c. f(m, n) m + n+1 d f(m, n) = |m|-|n|

Answers

Answer 1

The onto functions (surjective functions) are:

c. f(m, n) = m + n + 1.

At first we have to identify onto (surjective) functions from Z x Z to Z, we need to check if each element in the codomain (Z) has at least one preimage in the domain (Z x Z).

a. f(m, n) = 2m - n

This function is not onto because for odd numbers in the codomain (Z), there is no pair of integers (m, n) in the domain that will map to them.

b. [tex]f(m, n) = m^2 - n^2[/tex]

This function is not onto because for negative numbers in the codomain (Z), there is no pair of integers (m, n) in the domain that will map to them.

c. f(m, n) = m + n + 1

This function is onto. For any integer 'z' in the codomain (Z), we can find a pair of integers (m, n) in the domain such that m + n + 1 = z.

For example, if z = 0, we can choose m = 0 and n = -1, and then m + n + 1 = 0.

d. f(m, n) = |m| - |n|

This function is not onto because negative numbers in the codomain (Z) cannot be obtained from the domain (Z x Z).

For example, there is no pair of integers (m, n) in the domain that maps to -1.

Hence, The onto functions (surjective functions) are:

c. f(m, n) = m + n + 1.

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Related Questions

What is the unit rate of the equation below? y = 2x + 8

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Answer:

DF = 20.4

Step-by-step explanation:

The figure given is a kite.

A kite has two set of opposite sides that are congruent. And the diagonals bisect each other. Thus,

∆DEH is congruent to ∆FEH, therefore, DH = HF

Use pythagorean theorem to find DH:

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Include the appropriate unit in your answer.

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Answer:

Step-by-step explanation:

area of triangle = ½(base)(height)

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Answers

Answer:

Step-by-step explanation:

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Answers

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Answers

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Answers

Answer:

exponential!!! That is the answer if this is for Khan Academy!!

Divide.
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PLS HURRY IM SUPER CONFUSED

Answers

Answer: 487, B.

Step-by-step explanation:

24350 ÷ 50 = 487.

Divide :)

The answer is 487, or B.

P(A and B)
Hint:
Find P (Senior Boy)
P(B)
Classroom of Students
Boys Girls
Freshman 4
4 8
Sophomore 5 7 12
[?]
Junior 2 3 5
Senior 1
4 5
12 18
Please help :(

Answers

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

Number of boys = 12

Number of girls = 18

Total number of students = 12 + 18 = 30

Probability refers to chances of occurrence of any event.

Probability = Number of favorable outcomes ÷ Total number of possible outcomes

To find P(Senior | Boy), use [tex]P(A|B)=\frac{P(A\,\,and\,\,B)}{P(B)}[/tex]

P(Senior and Boy) = [tex]\frac{1}{30}[/tex]

P(Boy) = [tex]\frac{12}{30}[/tex]

So,

P(Senior | Boy) = P(Senior and Boy) ÷ P(Boy) = [tex]\frac{\frac{1}{30} }{\frac{12}{30} } =\frac{1}{12}[/tex]

Answer:

1/12

Step-by-step explanation:

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Answers

Answer:

216

Step-by-step explanation:

if she reads 24 books in 6 weeks

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Answer:

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Step-by-step explanation:

All these numbers are greater (or equal to) -6 because they are closer to 0

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Step-by-step explanation:

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Answer:

25 days

Step-by-step explanation:

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Answer:

Step-by-step explanation:

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1= 88°

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Answers

Answer:

4 percent

Step-by-step explanation:

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Q1. Butternut is a ski resort in Massachusetts. One of their triple chair lifts unloads 576 skiers per hour at the top of the slope. (A triple chair lift can carry three passengers per chair.) If 108 skiers are riding on the lift at any one time, how long does the ride from the bottom to the top take

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Answer:

11.25minutes

Step-by-step explanation:

From the question we are told that lifts unloads 576 skiers per hour at the top of the slope, this is expressed as;

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Answers

Answer:

m = -2/3

Step-by-step explanation:

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There’s an easy rule for this form !
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Answer:

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Step-by-step explanation:

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13 petunias

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Calculate the monthly share of annual expenses and find the total monthly expenses.

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Monthly share of Annual:

Total Monthly Expenses:

Answers

Answer:

918,14

Step-by-step explanation:

3,494.04

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788888

Step-by-step explanation:

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Answers

Answer:

permiteme veré en álgebra baldor

The roots of the equation f(x) = x² - 6x + 25 will be 3 - 4i and 3 + 4i.

What are the roots of the equation?

Let the equation be ax² + bx + c = 0. Then the roots of the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]

The quadratic equation is given below.

f(x) = x² - 6x + 25

Compare both the equations, then the value of a, b, and c will be 1, -6, and 25, respectively.

Then the roots of the equation are given as,

[tex]\rm x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4 \times 1 \times 25 }}{2 \times 1}\\x = \dfrac{6 \pm \sqrt{-64}}{2}[/tex]

Simplify the equation further, then we have

x = 3 ± 4i

The roots of the equation f(x) = x² - 6x + 25 will be 3 - 4i and 3 + 4i.

More about the roots of the equation link is given below.

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4 - 2/8 =
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Answers

Answer:

= 15/4

Step-by-step explanation:

4=32/8 so 32/8-2/8=30/8. 30/8 -> 15/4 or 3.75
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