Mathematics College

Functions:

In image 1: Evaluate the functions

In image 2: Given the functions, find their inverse, if possible and if not possible, redefine Domain or Range

Answers

Answer 1

Answer:

Image 1

1. x = 4

f(4) = (- 3*4 + 1) / 6 = -11/6

2. x = -2/3

f(-2/3) = -3*(-2/3) + 10 = 2 + 10 = 12

3. x = -5

f(-5) = [tex]\sqrt{-(-5)/20}[/tex] = [tex]\sqrt{5/20}[/tex] = [tex]\sqrt{1/4}[/tex] = 1/2Image 2To work out the inverse, substitute f(x) with x and x with y, then solve for y. The new function is the inverse of the given.

1. f(x) = 5x + 3

x = 5y + 3 ⇒ 5y = x - 3 ⇒ y = (x - 3)/5f⁻¹(x) = (x - 3)/5

2. f(x) = 4/5x

x = 4/5y ⇒ y = 5/4xf⁻¹(x) = 5/4x

3. f(x) = (2x + 7)/4

x = (2y + 7)/4 ⇒ 2y + 7 = 4x ⇒ 2y = 4x - 7 ⇒ y = 2x - 3.5f⁻¹(x) = 2x - 3.5

4. f(x) = (2x + 7) /(x + 3) = 2 + 1/(x + 3)

x = 2 + 1/(y + 3) ⇒ x - 2 = 1/(y + 3) ⇒ y + 3 = 1/(x - 2) ⇒ y = (1 - 3x + 6)/(x - 2) ⇒ y = (7 - 3x)/(x - 2)f⁻¹(x) = (7 - 3x)/(x - 2)

5. f(x) = [tex]\sqrt{x - 4}[/tex]

x = [tex]\sqrt{y - 4}[/tex] ⇒ x² = y - 4 ⇒ y = x² + 4f⁻¹(x) = x² + 4

Related Questions

3. What is 5⅕% of 325?

Answers

Answer:

20% × 325 =

(20 ÷ 100) × 325 =

(20 × 325) ÷ 100 =

6,500 ÷ 100 =

which expression is equivalent to x-5/3? 1/5√3^3 1/3√x^5 -3√x^5 -5√x^3

Answers

Answer:

What grade is this 12th?

Step-by-step explanation:

The equivalent expression for the expression given; (( 5/7 )² × (1/3)-³)-¹ is; (7/5)² • (1/3)³.

What is the equivalent expression for the given expression?

It follows from the task content that the expression which is equivalent to that which is given is to be determined.

here, we have,

Hence, since the given expression is; (( 5/7 )² × (1/3)-³)-¹;

It follows from the power of powers law of indices that we have;

( 5/7 )-² • (1/3)³

Also, according to the negative exponent law of indices; we have;

(7/5)² • (1/3)³.

On this note, the required equivalent expression is; (7/5)² • (1/3)³.

Read more on equivalent expressions;

brainly.com/question/24734894

#SPJ7

Use the figure to find the Volume.

Answers

Answer:

12π un^3

Step-by-step explanation:

Use the fomula: V= πr2 h

The radius is 2 and the height is 3.

I really don't know how to explain this but I can try, with a self- explanatory steps including the formula .

The work is in the screen shot goodluck.

Hope this helped!

Stay Safe!

Identify the sampling designs that use convenience sampling. Check all that apply.
Mr. Berkman asks all his third-period students about music preferences.
Each customer of a sandwich shop is interviewed about their customer satisfaction as they exit.
An online poll about voter opinion of political issues is posted on social media.
O A student organization interviews students in a lunch line about cafeteria meals.
Fifteen percent of families in the county are randomly chosen to respond to a survey about emergency services.
The management employees of a company, which has locations throughout the country, are asked about job
satisfaction.

Answers

Answer:

The answers are A,B, and D

Step-by-step explanation:

I got it right.

U.S. Manufactured General Aviation Shipments, 2009–2015
Year Qtr 1 Qtr 2 Qtr 3 Qtr 4 Total
2009 310 408 390 477 1,585
2010 243 377 281 433 1,334
2011 268 289 286 480 1,323
2012 305 358 339 514 1,516
2013 329 413 353 520 1,615
2014 345 380 379 527 1,631
2015 296 374 378 544 1,592

Click here for the Excel Data File

(a) Plot the data on airplane shipments.

Plot A Plot B Plot C Plot D

multiple choice 1
Plot A
Plot B
Plot C
Plot D

(b) Can you see seasonal patterns?

multiple choice 2
Yes
No

(c) Use MegaStat or Minitab to calculate estimated seasonal indexes and trend. (Round your answers to 3 decimal places.)

Qtr1
Index Qtr2
Index Qtr3
Index Qtr4
Index

(d) In which quarters are shipments highest? Lowest? (You may select more than one answer. Click the box with a check mark for the correct answer and double click to empty the box for the wrong answer.)

Highest

check all that apply 1
Q1
Q2
Q3
Q4

Lowest

check all that apply 2
Q1
Q2
Q3
Q4

(e) Is there a trend in the deseasonalized data?

There is a slight
(Click to select)
trend in the deseasonalized data.

Answers

Which of the following is in the solution set to 3x - y = 12? (hint: what
makes the equation true)
(3,2)
(0,4)
(-4,0)
(8,12)
Answer(8,12)

Answers

3(8)-12=12
24-12=12
The fourth choice.
Yeah I think you already got it

You buy egg yolks for $13/gallon. A batch of Hollandaise requires 4 oz of egg yolks. How much do you spend on egg yolks for one batch of Hollandaise?

Answers

Answer is in the photo. I can only upload it to a file hosting service. link below!

tinyurl.com/wpazsebu

a sector has a radius of 4 and a central angle of 40 degrees. Find the arc length and area of sector

Answers

Answer:

Step-by-step explanation:

θ = 2π/9 radians

arc length = rθ = 8π/9 units

area of sector = πr²/9 = 16π/9 square units

4) Find the area. 7 cm 9 cm 12 cm

Answers

Answer:

756 cm

i hope this helps

NEED MAJOR HELP FAST GET HERE QUICK PLEASE

Answers

A 45 degree angle is 1/8 of a circle, so keep that in mind for later. You're looking for the circumference of that 1/8 fence, so you have to use the formula, circumference/diameter=pi. Now, the problem gives you half the diameter, a.k.a the radius, so double it to get 44 ft. then, you multiply that by 3.14 (pi) to get 138.16. Now take the 1/8, from before, of the circumfrence and you get your final answer, 17.27 ft!

1/3 + 1/2 and I am 5 years old

Answers

Answer:

5/6

Step-by-step explanation:

Impossible Not Ukely Equslly Ukely & Unlikely Ukoly Certain Events: a. You will win the grand prize in a raffle if you purchased 2 of the 100 tickets. b. You will wait less than 10 minutes before ordering at a fast-food restaurant. c. You will get an even number when you roll a standard number cube. d. A four-year-old child is over six feet tall. e. No one in your class will be late to class next week. f. The next baby born at a hospital will be a boy, g. It will snow at our school on July 1. h. The sun will set today before 11:00 p.m. i. Spinning the spinner shown will result in green. j. Spinning the spinner shown will result in yellow.

Answers

Answer:

a. Unikely

b. Likely

c. Equally likely

d. Unlikely

e. Equally likely

f. Equally likely

g. Unlikely

h. Likely

i. No SPINNER SHOWN?

j. NO SPINNER SHOWN?

Step-by-step explanation:

I have no clue what the answer is please help

Answers

Don’t click or do anything to that file

an employer pays three workers x,y,z a total amount of 6100 a month. x is paid 125% of the amount y is paid; which represent 80% of the amount z is paid. how much does x receive a month

Answers

Answer: 2178.57

Step-by-step explanation:

Given

The employer pays 6100 total money a month

Suppose z receives A amount

Amount paid to y is 80% of A i.e.

[tex]\Rightarrow y=0.8A[/tex]

Amount paid to x is 125% of y i.e.

[tex]\Rightarrow x=1.25y=1.25\times 0.8A=A[/tex]

The Sum of their total money must be 6100

[tex]\Rightarrow A+0.8A+A=6100\\\Rightarrow 2.8A=6100\\\Rightarrow A=2178.57[/tex]

Amount receive by x is 2178.57

What is the interest you will pay if you borrowed $120 at 5% interest for 6 years?

Answers

Answer:

Hope this helps!

Step-by-step explanation:

We will need the loan payment formula:

That formula is really complex and we expect you to solve it.

Your monthly payment would be $1.93 per month for 6 years making the TOTAL loan cost 1.93 * 12 * 6 = 138.96

Since the principal you borrowed is $120 the total interest =

(138.96 minus 120.00) which equals $18.96

Answer:

The answer is 36

Step-by-step explanation:

120*0.05=6

6.6=36

In what direction is the line containing the points (-4, 3) and (-4, 14) going?
A. horizontal
B. vertical
C. up and to the left
D. down and to the right

Answers

Answer:

A. horizontal because -4 and -4 are on the same line... it's coordinate planes it's always over then up so your line will be horizontal going from 3 to 14

find the perimeter and area of the polygon with E(0, 0), F(7, 0), G(7, 2), H(0, 2)

Answers

i think not sure sorry if i got it wrong but ya

Answer:

15 hope it's helpful sorry I think it's 15 if it's wrong sorry

6 1/5 - 4 2/4=? help I need it now pls thx u.

Answers

exact form: 17/10
decimal form: 1.7
mixed number form: 1 7/10

The expression (g^2)^4 is equivalent to g^m. What is the value of m?

^ means exponents

Answers

Answer:

m = 8

Step-by-step explanation:

4 x 2

you just have to multiply exponents

Identify the distance between points (−1,7,10) and (6,−3,2), and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary.

Answers

Answer:

d ≈ 14.6 units; M (2.5, 2, 6)

Step-by-step explanation:

Using the distance formula for 3-D dimensions, you get the √(213) which equals 14.6

Then, using the midpoint formula for 3-D dimensions, you find the coordinates 2.5 for x, 2 for y, and 6 for z.

CCBC is planning to purchase a total of 500 blue and gold balloons to decorate for
graduation. They want three times as many blue balloons as gold balloons. How
many of each should they buy?

Answers

Explanation is in the file

tinyurl.com/wpazsebu

someone please find the area of this figure.

Answers

Answer:

to answer this question you have to first split up the diagrams,I'm to lazy to do that but I'll try

area of rectangle- 2mm×4mm=8mm²

area of rectangle 2-6mm×3mm=18mm²

area of rectangle 3- 4mm×2mm=8mm²

area of triangle =1/2 b×h

=1/2×6×18

=54mm²

total area = 8mm²+18mm²+8mm²+54mm²

=88mm²

Question 8 is the one I’m having trouble on it

Answers

Just multiply 30 times 2,000 and also multiply 30 times 700. The reason you will multiply it by 30 is because in 1 month there is 30 days. 30 x 2,000= 60000 30 x 700 = 21000 I’m only 9 btw so sorry if I didn’t give a lot of detail lol

Pls solve this for me!! ^^

Answers

Answer:

-10

Step-by-step explanation:

[tex]5(a-b)\\\\5(-4-(-2))\\\\5(-4+2)\\\\5(-2)\\\\\boxed{-10}[/tex]

Hope this helps!

Label the diagram
with
x-axis y-axis origin quadrant I quadrant II quadrant III quadrant IV
A
B
C
D

Answers

A) y-axis

B) quad lll

C) x-axis

D) quad IV

Is this the answer you were looking for?

A) y-axis

B) quad lll

C) x-axis

D) quad IV

Is this the answer you were looking for?

12x+6n-36 in standard form

Answers

6n+12x-36 . hope this helps

Не
На спортивных соревнованиях по Плаванию за первое
место боролись Вера, Ксюша, Алина
Алина и Надя. Коша
заняла
Второе место, Надя не заняла ни первое,
НИ второе место, Вера заняла четвёртое место, Алина
Не заняла первое место.
Кто из девочек стал победителем соревнований?

Answers

Answer:

I don't know the answer

Step-by-step explanation:

rkvjtjxkfkekzdk kdkvkf

In AIJK, i = 270 cm, j = 170 cm and _K=122°. Find the area of AIJK, to the
nearest square centimeter.

Answers

9514 1404 393

Answer:

19,463 cm²

Step-by-step explanation:

The area is given by the formula ...

A = (1/2)ij·sin(K)

Filling in the values, we find the area to be ...

A = (1/2)(270 cm)(170 cm)·sin(122°) ≈ 19,463 cm²

What is the domain of the volume function?
(0,00
(3,5)
c. (3,
D.
(0,3

Answers

Answer:

it is 3,5

Step-by-step explanation:

check the domain of the volume

What number divided by 4 equals 6?
Type the correct answer, then press Enter.

Answers

Answer:

Step-by-step explanation:

Let x be the number.

[tex]x/4=6[/tex]

Multiply both sides by 4 to isolate x

[tex](x/4)4=6*4\\x=24[/tex]

I hope this helps!

Other Questions

help please asap!!!have a good day Neon Light Company of Kansas City ships lamps and lighting appliances throughout the country. Ms. Neon has determined that through the establishment of local collection centers around the country, she can speed up the collection of payments by two days. Furthermore, the cash management department of her bank has indicated to her that she can defer her payments on her accounts by one-half day without affecting suppliers. The bank has a remote disbursement center in Florida. a. If Neon Light Company has $2.55 million per day in collections and $1.11 million per day in disbursements, how many dollars will the cash management system free up? (Enter your answer in dollars not in millions (e.g., $1,234,567).)b. If Neon Light Company can earn 7 percent per annum on freed-up funds, how much will the income be? (Enter your answer in dollars not in millions (e.g., $1,234,567).)c. If the total cost of the new system is $430,000, should it be implemented?YesNo The following cards are used in a game. If each of the cards is turned over and shuffled, then how much of a greater chance is there in drawing a spade over drawing a 7? write any two functions to be performed by illiterate person Find the measure of angle F How many electrons and protons does the sodium ion have 11 protons and 11 electrons A 6-sided number cube is rolled 120 times and 4 is rolled 23 times. Based on the data, what is the best estimate of the probability that the next roll will be a 4?A. 1/6B. 1/3C. 1/4D. 1/2 The molecular weight for the compound from the previous question is64.07 g/mol. What is its molecular formula? 26. Name one positive effect and one negative effect of the Columbian Exchange, WILL GIVE BRAINLISTTT!!!!! What issues confronted Texas governors during the 1930s, and what actions did the governors take? Write a paragraph- "Our National Flag". What do you mean by National Flag?. What does our National Flag symbolize?. How have we got our National Flag?.What is its length and breadth? .Which memory do red and green colours bear?.When do we hoist our National flag?.Where is it hoisted?.When is the national flag half-mast?.How can we protect and uphold the honour of our national flag? .How do you feel for your national flag?In this question What is the y value in solution the following system?4x+3y=7X+2y=-2(Worth 10 points) Which of the following is a dangerous health condition characterized by the hardening of the arteries and a decreased blood flow?Coronary artery diseaseAtherosclerosisCerebral vascular diseaseAll of the above alex works for his father assembling clock motors he is paid a piecework rate of $8.50 per motor. this week he assembled 21 motors HEEEEEEEEEELPPP I NEED ANSWER HELPA bakery sold 154 mocha cupcakes in a day, which was 35% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day? 3. B = {2, 4, 6, 8, 10}AU B = {1, 2, 3, 4, 6, 8,10 }An B = {2,4}Represent the above information on a Venn diagram.Please help If RS is parallel to AB, what is the width of the sand trap?a. 149 b. 82 c. 107 d. 84 please helpppp En una competicin participan 200 atletas, 2/5 son espaoles, 1/3 del resto son franceses, 35 son alemanes y el resto son ingleses. Cul es la fraccin de atletas alemanes que hay? how to describe your school Does anyone know this??

Functions: In image 1: Evaluate the functions In image 2: Given the functions, find their inverse, if possible and if not possible, redefine Domain or Range

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Functions:

In image 1: Evaluate the functions

In image 2: Given the functions, find their inverse, if possible and if not possible, redefine Domain or Range