Determine the inverse function of f(x)=1/7x-1/7​

Answers

Answer 1

The inverse of the function → y= f(x) = 1/7x - 1/7​ is -

f⁻¹(x) = 7x + 1.

We have -

y = f(x) = x/7 - 1/7

We have to find its inverse function.

What is the procedure to find inverse of function ?

Inverse of a function can be calculated by following the steps mentioned below -

Step 1 -  Replace 'y' with 'x' and vice - versa.

Step 2 - Rewrite the equation by solving for 'y'.

Step 3 - Replace 'y' with f⁻¹(x).

According to the question, the equation given is as follows

y = f(x) = x/7 - 1/7

Replace 'y' with 'x', we get -

x = y/7 - 1/7

Now, solve for y -

y/7 = x + 1/7

y = 7(x + 1/7)

y = 7x + 1

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = 7x + 1

Hence, the inverse of the function → f(x) = 1/7x - 1/7 is -

f⁻¹(x) = 7x + 1.

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Related Questions

Simplify the the following

Answers

Answer:

Answer is in the picture attached

In the metric system, how many milligrams are needed to make a gram?

Answers

Answer:

In one gram, there are 1000 milligrams.

To convert g to mg, multiply the gram value by 1000.

What is the mean and the median of 2, 4, 6, and 8?

Answers

Mean
2+4+6+8=20
20/4=5

Median
2,4,6,8

*4+6=10
10/2=5

Evaluate.
4-6 |3-5| /3

Answers

Answer:

0

Step-by-step explanation:

I need help −1/1/5+(−3/5)=

Answers

Answer:

- 4/5 /decimal form -0.8

Step-by-step explanation:

-9/5 is the answer or -1.8

Jonah read 5 1/2 chapters in his book in 90 minutes. How long did it take h
to read one chapter?

Answers

16.36363636363636 so approximately 17 minutes

value of x in the equation −3(3x−4)=15−8x?

Answers

Answer:x=−19

Step-by-step explanation: work in your head ppl

Answer: -3

Step-by-step explanation:

trust me

Suppose Aji and sunshine have to pay $11 in royalties for each Beatles song and $7 for each Donovan song. How many of each type should they put on their CD to minimize their royalty costs?

Answers

To minimize their royal costs to $200, the number of Donovan songs to include is 15 and the number of Beatles songs to include is 5.

What are ratios?

Ratios are numerical relationships between variables that show how much each variable is contained in another.

Ratios are stated in fractions, percentages, or decimals.

Data and Calculations:

Total songs to include in the song = 20

The ratio of Donovan and Beatles = 5:1.5

The number of Donovan songs to include = 15 (20/6.5 x 5)

The number of Beatles songs to include = 5 (20/6.5 x 1.5)

Royalty cost per Donovan song = $11

Royalty cost per Beatles song = $7

Total royalty costs for Donovan and Beatles song = $200 ($11 x 15 + $7 x 5)

Thus, the number of Donovan songs to include is 15 and the number of Beatles songs to include is 5.

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Question Completion:

Aji and Sunshine want to make a CD of songs from the 1960s to donate to their school library to be broadcast during school picnics. Sunshine's parents were big fans of the 60s singer Donovan, and they named her after his song "Sunshine Superman." Aji's folks were devotees of the Beatles. Aji and Sunshine want their CD to consist entirely of songs by Donovan and the Beatles. Because Sunshine is named after a Donovan song, she wants to include at least as many Donovan songs as Beatles songs. Aji agrees. In return, Sunshine agrees to include at least five Beatles songs. 5 1.5 To provide enough variety to make the mix interesting, they decide to include at least 20 songs altogether.

Solve the equations and check the results a. 4x+5=17-2x

Answers

4x+2x=17-5
6x=12
X=12:6
X=2

Find the circumference of the largest circle that will fit inside of a square that has an area of 144 square feet?

Answers

Answer:

6

Step-by-step explanation:

The square's side will be √144 = 12

The largest circle will have diameter of 12 so it's radius will be 12/2 = 6

an independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. they collected information on the percentage of the bill left as a tip for 2525 randomly selected bills. the average tip was 13.1.1% of the bill with a standard deviation of 2.6%2.6%. assume that the tips are approximately normally distributed. construct an interval to estimate the true average tip (as a percent of the bill) with 90% confidence. round the endpoints to two decimal places, if necessary.

Answers

90% confidence interval is 11.65 <µ< 114.566 as per standard deviation data.

What is a standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.

Sample mean (T) = 13.11%

Sample standard deviation (s) = 2.6

Sample size (h) = 25

significance level = α = 1 -0.90 = 0.1

Degrees of freedom for t- distribution (df) = 24

Critical value = ta/2

df = [tex]t_{0.1}[/tex], df=24 = ±2.80

The margin of error (E) =[tex]t_\frac{a}{2} , df\frac{s}{\sqrt{h} }[/tex]

E=2.8X [tex]\frac{2.6}{\sqrt{25} }[/tex] =1.456

Limits of 90%. Confidence Interval is.

Lowest limit = X' - E = 13.11-1.456 = 11.65

Upper limit= X' + E = 13.11+1.456 = 14.566

90% confidence interval is 11.65 <µ< 114.566 as per standard deviation data.

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2. Is 4x-3=19 true, false, or open? (1 point)
true
false
Open

Answers

True, I took the quiz

Underground Floors charges $8 per square foot of wood flooring plus $150 for installation. Woody's Hardwood Flooring charges $6 per square foot plus $200 for installation. At how many square feet of flooring would the two companies charge the same amount for flooring? If you were going to put flooring on your kitchen floor that had an area of 120 square feet, which company would you choose?

Answers

AT 25 SQUARE FEET OF FLOORING

CHOOSE WOODY'S HARDWOOD FLOORING

HOW TO COMPARE RATE OF FLOORING OF TWO COMPANY ?

Typically, the price of engineered hardwood flooring is $6 to $10 per square foot, plus $1.75 to $2.20 per square foot for installation. High-quality hardwood flooring typically costs between $6 and $13 per square foot from customers. Your home renovation project could be very stressful. Expectations, timeframes, budgets, and the cost of flooring contractors all need to be harmonized.

There will always be a time when you want to give up on the renovation project. For some reason, finding someone to install your flooring is usually the first step.

CALCULATION

1 - 8s + 150 = 6s + 200

      2s = 50

         s= 25 sq.feet

2 - 120 * 8 + 150 = 1110

      120 * 6 + 200 = 920

1110 > 920

so choose woody's hardwood flooring.

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Simplify the following. (Do NOT evaluate!) √80y^3

Answers

After simplifying the expression √80y³, we get the answer as 4 y √5 y.

We are given that:

√80y³

We have to simplify it.

We will first make the factors of it.

Factors of 80:

80 = 2 × 2 × 2 × 2 × 5

Factors of y³:

y³ = y × y × y.

Now the expression can be re- written as:

√2 × 2 × 2 × 2 × 5 × y × y × y.

Simplifying it:

2 × 2 × y √5 y

4 y √5 y

Therefore, after simplifying the expression √80y³, we get the answer as 4 y √5 y.

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the area of the rectangle is 14yd squared and the length of the rectangle is 3yds leass than twice the width

Answers

The dimensions of the rectangle are:

Length = 7/2 ydWidth = 4 ydTotal area = 14 yd²

What is the area?The quantity area expresses the extent of a region on a plane or curved surface. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

To find the dimensions of the rectangle:

Let,

Area = A = 14Width = wLength = 2w-3A = lwA = (2w-3)w

Extend the area equation as follows:

A = 2w2-3w

Rearrange:

2w2 - 3w - A = 0

Substitute known information for A:

2w2 - 3w - 14 = 0

To solve quickly, factor the left side (or use the quadratic formula):

(w+2)(w - 7/2) = 0

The factorial solutions for w are -2 and 7/2.

Assuming this is a genuine rectangle, the width must be positive.

As a result, the length is:

2(7/2) - 3

That is,

7 - 3 = 4

Therefore, the dimensions of the rectangle are:

Length = 7/2 ydWidth = 4 ydTotal area = 14 yd²

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The complete question is given below:
The area of a rectangle is 14 yd², and the length of the rectangle is 3 yd less than double the width. find the dimensions of the rectangle.

What
is the slope of the line that passes through the points (-4, 6) and (-4, 18)?
Write your answer in simplest form.

Answers

Undefined slope because there is no change in c values meaning the denominator of the slope is zero
And that makes it undefined

If the 100th term of an arithmetic sequence is 609, and its common difference is 6, then
its first term a1=
It’s second term a2=
It’s third term a3=

Answers

Answer:

15, 21, 27

Step-by-step explanation:

[tex]a_n}[/tex] = [tex]a_{1}[/tex] + (n-1)d  

[tex]a_{n}[/tex] is the number in the sequence we are looking for

[tex]a_{1}[/tex]  This is the first term in the sequence that we do not know and we are looking for

n stands for the number of the term and d is the common difference.  We will put in all that we know and solve for the first term.

609 = [tex]a_{1}[/tex] + (100-1)6  

609 =[tex]a_{1}[/tex] + (99)6

609 = [tex]a_{1}[/tex] + 594  Subtract 594 from both sides of the equation

15 = [tex]a_{1}[/tex]

Now that we know that the first term is 15 we just add 6 to get the next term which is 21 and then add 6 again to get the last term 27.

WILL CHOOSE BRAINLIEST!!!

Answers

Answer: 51.96m

Step-by-step explanation:

We can solve this using cosine, remember SOHCAHTOA, so cos is adjacent over hypotenuse.

hyp = 60

adj = ?

[tex]cos = \frac{adj}{hyp}\\cos 30 = \frac{x}{60} \\\\cos30 *60=x\\x=51.96m[/tex]

Answer: 51.96m. This is going to be the answer

f(x)= 3x - 2 and g(x) = 2x+1

Answers

Answer:

What do I solve for with these functions?

Step-by-step explanation:

identify whether the statement describes inferential statistics or descriptive statistics. the average age of the students in a statistics class is 20 years.

Answers

The statement ''The average age of the students in a statistics class is 20 years'' describes descriptive statistics.

As they're used to represent a particular records set, metrics like average, median, mode, standard deviation, and variety are categorized underneath descriptive information.however, when a speculation check is carried out to make inferences about a population from sample records, it's miles known as inferential data.As right here we're given the average age of all 20 students in the magnificence right here, and we are not seeking to prediction from the sample records, and we're directly getting it as a population parameter. therefore descriptive statistics is the correct solution here.via creating summaries of records samples, descriptive statistics can be used to describe the characteristics of a facts set.

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choose the first set in the list of natural​ numbers, whole​ numbers, integers, rational​ numbers, and real numbers that describes the following number.

Answers

The given number is a real number.

What are real numbers?

A real number is a value of a continuous quantity that can be used to indicate a distance along a line in mathematics.

We are given the following in the question:

{natural​ numbers, whole​ numbers, integers, rational​ numbers, real numbers}

π / 108

We have to tell the type of number that describes the given fraction.

Evaluating the value, we have,

0.0290888208666...........

This is not a natural number or a whole number. This is not a rational number.

Since is an irrational number, thus quotient of an irrational number and a rational number is an irrational number.

Thus, it is a real number.

The complete question is given below:-

Choose the first set in the list of natural​ numbers, whole​ numbers, integers, rational​ numbers, and real numbers that describes the following number. StartFraction pi Over 108 EndFraction.

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At a local recreation center, there were 36 people working out, 18 people swimming, and 27 were playing basketball. What percentage of people were there to swim? Round your answer to the nearest tenth.

Answers

Answer:

22.2%

Step-by-step explanation:

Total number of people at the recreation center=81

Number of people swimming=18

=18/81 x 100

=22.22222

Round of to the nearest tenth

=22.2%

The length of a rectangle is 6 inches longer than its width. What are the possible widths if the area of the rectangle is at least 667 square inches?

Answers

Answer:

D, [tex]w\geq 23[/tex]

Step-by-step explanation:

The length is 6 inches longer than it's width, therefore:

[tex]l=w+6[/tex]

The area of the rectangle is AT LEAST 667 square inches, so:

[tex]lw\geq 667[/tex]

Now, we have a system of two equations:

[tex]\left \{ {{l=w+6} \atop {lw\geq 667}} \right.[/tex]

We want to isolate the width, so substitute the first equation into the second to eliminate the length.

[tex](w+6)w\geq 667[/tex]

Simplify:

[tex]w^2+6w\geq 667[/tex]

Since we now have a polynomial equation that needs to be factored, set the value of one side to 0.

[tex]w^2+6w-667\geq 0[/tex]

Now factor the equation:

[tex](w-23)(w+29)\geq 0[/tex]

Taking each factor individually, we find the following:

[tex]w\geq 23\\w\geq -29[/tex]

Since a negative width doesn't make any sense, we can eliminate that solution, and we are left with the correct answer!

[tex]w\geq 23[/tex]

How are defined terms and undefined terms related?

Answers

Answer:

"Defined items" are defined in terms of "undefined terms".

Step-by-step explanation:

None.

Which graph does not represent a function?

Answers

Answer:

Choice 3

Step-by-step explanation:

The graph fails the vertical line test.

What is the difference between positive association and negative association as it pertains to the relationship between two​ variables?.

Answers

A positive association occurs when an increase in one variable is generally associated with the increase in the second variable and a negative association occurs when one variable tends to decrease as the other increases.

What is meant by an association relationship between two variables?

An association is any relationship between two factors that produces them subordinate, i.e. knowing the value of one variable gives us some data around the possible values of the moment variable.

The objective of this variable is to utilize clear measurements and visualisations to investigate affiliations among different kinds of factors.

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What is the simplified form of the quantity x over 4 plus y over 3 all over the quantity x over 3 minus y over 4?

Answers

The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y).

What is an expression?

An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.

For example 3x +5y

Given the phrase,

x over 4 = x/4

y over 3  = y/3

Combine x/4 + y/3

x over 3 minus y over 4 = x/3  - y/4

Therefore ;

(x/4 + y/3) ÷ (x/3  - y/4)

⇒ (3x + 4y)/12 ÷ (4x - 3y)/12

The second fraction will inverse in multiplication

⇒ (3x + 4y)/12 × 12/(4x - 3y)

⇒ (3x + 4y) / (4x - 3y).

Hence "The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y)".

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What is constant in the simplified form of (x - 6)²?

Answers

Answer:

36

Step-by-step explanation:

The constant is the number when complete simplified, which in this case would be only formed by squaring the 6, equaling 36.

Hope this helps! :)

Answer: +36

Step-by-step explanation:

(x - 6)² simplified: x^2 -12x + 36

The constant in this algebraic expression is 36 because it's value or number doesn't change in the expression (x^2 -12x + 36)

I really need help on 16 and 18 I'm super confused problem because I'm tired but I really need help ​

Answers

Answer:

Hello,

Step-by-step explanation:

16)

Area of the square= 5²=25 (unit of square)

17)

Volume of the cube =3^3 =27 (unit of volume)

18)

side of the cube =5 (unit of lenght)

Volume of the cube = (5 (unit of lenght)) ^3

=125 * (unit of lenght)^3 =125 (unit of volume)

3.
According to the 2010 census, the population of Nebraska was 1.8 x 106 people. Which state
had a smaller population?
OCalifornia: 3.7 × 107
ORhode Island: 1.1 × 106
OTexas: 2.5 x 107
OMissouri: 6 x 106

Answers

If the population of Nebraska was 1.8×[tex]10^{6}[/tex], then the state which had a smaller population is Rhode Island

Given,

The population of Nebraska = 1.8×[tex]10^{6}[/tex]

The population of Rhode Island = 1.1×[tex]10^{6}[/tex]

1.1×[tex]10^{6}[/tex] <  1.8×[tex]10^{6}[/tex]

So, Rhode island has population less than Nebraska

Hence, if the population of Nebraska was 1.8×[tex]10^{6}[/tex], then the state which had a smaller population is Rhode Island

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