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
kogti [31]
3 years ago
6

For each of the following functions, determine if they are injective. Also determine if theyare surjective. Also determine if th

ey are bijective.No justification needed.The firstthree have already been filled out for you, as an example. Also, recall interval notation:[a,b] ={x∈R:a≤xandx≤b}. You should be able to come up with a similar definitionfor (a,b) and (a,b] and [a,b).1.f:R→R, f(x) =x2.f:R≥0→R, f(x) =x+ 13.f:R≥0→R, f(x) = cos(x)4.f:R→R, f(x) =ex5.f:R→R, f(x) =2xifx≥0−x2ifx <0.6.f:R→(0,[infinity]), f(x) =ex7.f:R≥0→R≥0, f(x) =x48.f:{−1,2,−3}→{1,4,9}, f(x) =x29.f:R≥0→[−1,1], f(x) = cos(x)10.f: [0,π]→[−1,1], f(x) = cos(x)11.f:R≥0→[−1,1], f(x) = 012.f: US Citizens→Z, f(x) = the SSN ofx.13.f: US Zip Codes→US States, f(x) = The state thatxbelongs to.

Mathematics
1 answer:
timurjin [86]3 years ago
7 0

Answer:

Check below

Step-by-step explanation:

1. Definition for intervals

(a,b)=\left \{ x\in\Re : a

2. Functions

1) \Re \rightarrow \Re \\ f(x)=x

Let's perform graph tests.

That's an one to one, injective function. Look how any horizontal line touches that only once. Also, It's a surjective and a bijective one.

2)\Re\geq0\rightarrow\Re , f(x)=x+1\\

Injective, surjective and bijective.

Injective: a horizontal line crosses the graph in one point.

3)f:\Re\geq 0\rightarrow\Re, f(x) = cos(x)

The cosine function is not injective, bijective nor surjective.

4)f:\Re\rightarrow\Re \:f(x)=ex

Since e, is euler number it's a constant. It's also injective, surjective and bijective.

5)  Quite unclear format

6) \:f:\Re\rightarrow(0,\infty), f(x) =ex

Despite the Restriction for the CoDomain, the function remains injective, surjective and therefore bijective.

7) f:\Re\geq 0 \rightarrow  \Re\geq0, f(x) =x^{4}

Not injective nor surjective therefore not bijective too.

8).f:\{-1,2,-3\}}\rightarrow \{1,4,9\}, f(x) =x^{2}

f(-1)=1, f(2)=4, f(-3)=9

Injective (one to one), Surjective,  and Bijective.

10) f:\Re\geq 0\rightarrow [-1,1], f(x)= cos(x)\\-1=cos(x) \therefore x=\pi,3\pi,5\pi,etc.

Surjective.

11.f:R\geq 0[-1,1], f(x) = 0\\

Surjective

12.f: US Citizens→Z, f(x) = the SSN of x.

General function

13.f: US Zip Codes→US States, f(x) = The state that x belongs to.

Surjective

You might be interested in
Create a dot plot showing a uniform distribution.
Marina86 [1]

Answer:

You can also use a dot plot to identify the shape of a distribution. All the dots are about the same height. A uniform distribution is also symmetric. The data on the right of the distribution are approximately a mirror image of the data on the left of the distribution.

5 0
3 years ago
Help me please! :)<br> ㏒(4x)=2
Ray Of Light [21]
Answer: x=25 work below :)

4 0
3 years ago
Rueben sells electronics. He earns a 5% commission on each sale he makes. If Ruben wants to make $100 in commission, what is the
Alecsey [184]

Answer:

It is 20

Step-by-step explanation:

7 0
3 years ago
172% of 50 is what number?
Likurg_2 [28]

Answer:

172% of 50 means 172÷100 multiplied by 50 will give you 86

6 0
2 years ago
Read 2 more answers
Find the distance speed=72km/h time=45mins
butalik [34]

The distance is 54 km if the speed and time are 72 km/h and 45 minutes respectively.

<h3>What is distance?</h3>

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

Speed = 72 km/h

time = 45 mins = 45/60 = 0.75 hours

We know,

Distance = Speed×time

Distance = 72(km/h)×0.75(h)

Distance = 54 km

Thus, the distance is 54 km if the speed and time are 72 km/h and 45 minutes respectively.

Learn more about the distance here:

brainly.com/question/26711747

#SPJ1

8 0
2 years ago
Other questions:
  • They spent $16.00 per basketball and $24.00 per football, spending a total of $480.00. They bought 5 more footballs than basketb
    13·1 answer
  • (Only number one) !!PLEASE EXPLAIN HOW TO SOLVE DON’T JUST TELL ME THE ANSWER!!
    9·1 answer
  • (xy + 9y + 2) and (xy – 3)
    8·1 answer
  • A point is reflected over the y-axis, but the x-coordinate does not change. What is the location of the point?
    9·1 answer
  • Brads statement shows a previous balance of $2592.35, a payment of $75, and new transactions totaling $432. His APR 18.6%. What
    14·1 answer
  • 1. What is the product of 6.8 and 4.7?<br> A. 3.196<br> AB. 31.96<br> C. 319.6<br> D. 3196
    11·2 answers
  • Substitue the expression 5-3x into the second equation
    13·1 answer
  • mrs. Kenny teaches a ceramics class. She finds that she has 7/8 of a pound clay project. The project requires 1/6 of a pound. ho
    8·1 answer
  • (4rxt – 8r2x + x²) – (6rx² + 5rxt – 2x)
    11·1 answer
  • What is 357 times 1045?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!