Let f be the function defined by f(x)=x3+x2+x. Let g(x)=f−1(x), where g(3) = 1. What is the value of g'(3)?.

Answers

Answer 1

Quick review of the inverse function theorem:

By definition of inverse function,

f(f⁻¹(x)) = x

Differentiating both sides with respect to x using the chain rule gives

f'(f⁻¹(x)) • (f⁻¹)'(x) = 1

so that the derivative of the inverse is

(f⁻¹)'(x) = 1 / f'(f⁻¹(x))

Now if f(a) = b and a = f⁻¹(b), then the theorem says

(f⁻¹)'(b) = 1 / f'(a)

so that

g'(3) = 1 / f'(1)

We have

f(x) = x³ + x² + x   ⇒   f'(x) = 3x² + 2x + 1   ⇒   f'(1) = 3 + 2 + 1 = 6

and so

g'(3) = 1/6


Related Questions

Which lines from the passage present the most likely reason that theodora’s attitude changes?.

Answers

The lines from the passage refers to a change in Theodora's attitude towards divorce law.

She made some amendments to the law in order to provide benefit to young girls who are suffering from masculine powers.

She was also against the girls trafficking and she saved young girls from being victim of human trafficking. She was the first ruler to recognize rights of woman.

Learn more at https://brainly.com/question/25467739

The equilibrium constant for the reaction cu + 2ag.

Answers

Answer:

Socratic app

Explanation:

it will help you

If the weight of an object on earth is 245 n, what must be the mass of the object?.

Answers

Answer:

128

Explanation:

One of the lady spartans was falling to the ground.

Answers

What does that mean?

According to Wilson, which of the following groups had too much power over the US economy and government? socialists big business workers Congress.

Answers

Woodrow Wilson was of the opinion that when it came to power over the b, Big Business had too much of it.

Woodrow Wilson was not a fan of the power that big business had in the U.S. and so to combat it he introduced:

The Federal Trade Commission Act Clayton Antitrust Act

These two acts were meant to reduce the monopolistic tendencies of big business in the United States and to increase competition in the market for the betterment of the American people.

In conclusion, Wilson was against big business.

Find out more at https://brainly.com/question/11851810.

Answer:

Big business

Explanation:

on edge 2021

Most individuals and businesses are likely to find their judicial interactions in _____.

Answers

Answer:

State courts

Explanation:

A product is marked down 15%; the sale price is $127. 46. What was the original price?.

Answers

Answer:

849.73 is the correct answer to the

question

Anthony would like to have his brokerage firm handle more of his financial needs because he has been pleased with the service provided when he bought and sold stocks and bonds. If he explores the services offered by such firms in more depth, he will find that.

Answers

There are firms that handles the financials for people. If he explores the services offered by such firms in more depth, he will find that:

The brokerage firms are becoming serious competitors for banks and other depository institutions by offering high-yield combination savings and checking accounts and money market accounts, as well as certain types of loans.

Brokerage firms often helps individuals or firms in providing some key financial services.   A full-service brokerage firm is known to be a brokerage firm that gives a range of financial services and also to gives room for one to buy and sell securities.

They help customers with financial planning services as well as consulting services and also provide trust services and wealth management services.

See full question below

Anthony would like to have his brokerage firm handle more of his financial needs because he has been pleased with the service provided when he bought and sold stocks and bonds. If he explores the services offered by such firms in more depth, he will find that:

federal laws prohibit brokerage firms from competing with banks, savings and loan associations, and credit unions.

although brokerage firms can offer some banking services, they typically are less efficient at providing them than banks, because they specialize in buying and selling securities.

brokerage firms are becoming serious competitors for banks and other depository institutions by offering high-yield combination savings and checking accounts and money market accounts, as well as certain types of loans.

although brokerage firms offer attractive banking services, federal law prohibits individual investors from holding both a checking account and a securities account with the same firm.

Learn more from

https://brainly.com/question/2494366

why do fishes smell a lot

Answers

Answer:

When fish are killed, bacteria and fish enzymes convert TMAO into trimethylamine, which makes the fish oder smell

Explanation:

Answer:

their apart of the ocean so their naturally smelly

What should you do when a garbage can is nearly full.

Answers

Answer:

You can also place a false bottom inside the trash can to stop overfilling. To do that, simply place an object like a cardboard box underneath and outside the bag so that when it appears full it will not be as heavy as a bag that reached all the way to the bottom.

Explanation:

(winks and runs off)

When the garbage can is full, it is transferred into bigger dustbins that are placed outside the houses.

What is garbage management?

Domestic composting, recycling, reusing, and burning or burying of waste in their own yards are all examples of on-site household waste management. Off-site household waste management consists of delivering separated recyclables to drop-off locations, dumping at a landfill or in public trash cans, or making donations.

The environment is protected from the hazardous effects of the inorganic and biodegradable elements included in trash via waste management. Air pollution, soil erosion, and water poisoning can all result from improper waste management. If waste is collected and managed well, it can be recycled.

Therefore, when the trash container is full, it is moved into larger trash containers that are positioned outside the homes.

To learn more about the garbage disposal, refer to the link:

https://brainly.com/question/19813331

#SPJ5

To what extent were the goals of reconstruction regarding african-americans achieved by 1900?.

Answers

Answer: The goals were

ensure citizenship and civil liberties , Provide economic , and Provide education opportunities for former slaves

Explanation:civil right act in 1866

What atomic or hybrid orbitals make up the sigma bond between sb and f in antimony(iii) fluoride, sbf3?.

Answers

Answer:

Sb electronic configuration is [Kr]4d105s25p3

It can undergoes sp3 hybridisation

sigma bond is formed between Sb & F in antomony (III) fluoride SbF3 is

"sp3 hybrid orbital of Sb + 2p - orbital of F".

the approximate F-Sb-F bond angle is 1070

Explanation:

A deal is a deal, so here is a good one, let's see who gets it right. I had $10. 0. My mom gives me $30. 00, my dad gave me $30. 0. My aunt and uncle give $100. 0. I had another $10. 0. How much money did i have? the right answer will be deleted & you will be asked to repost the question on your page.

Answers

Answer:

the answer to your question is 180

Which detail from the passage best supports the idea that mr. Jones is a reckless farmer? "the uproar awoke mr. Jones, who sprang out of bed" "everyone fled to his own sleeping-place. " "making sure that there was a fox in the yard" "let fly a charge of number 6 shot into the darkness".

Answers

The detail from the passage best supports the idea that Mr. Jones is a reckless farmer is "let fly a charge of number 6 shot into the darkness". Thus, option fourth is correct.

What is the meaning of reckless?

The term reckless is derived from the Old English word receleas, which means "careless, thoughtless, or heedless."

"Let go a charge of Number 6 shot into the night," according to George Orwell's text, best supports the assumption that Mr. Jones is a reckless farmer.

Mr. Jones is in charge of the Manor Farm before the animals take over and rename it Animal Farm. He is frequently inebriated. He is cruel to animals who are hungry. He stands in for Tsar Nicholas II, who was deposed by the Revolution. Therefore, option fourth is correct.

Learn more about reckless here:

https://brainly.com/question/28618592

#SPJ5

The detail from the passage best supports the idea that Mr. Jones is a reckless farmer is "let fly a charge of number 6 shot into the darkness". Thus, option D is correct.

What is the meaning of reckless?

The term reckless is derived from the Old English word receleas, which means "careless, thoughtless, or heedless."

"Let go a charge of Number 6 shot into the night," according to George Orwell's text, best supports the assumption that Mr. Jones is a reckless farmer.

Mr. Jones is in charge of the Manor Farm before the animals take over and rename it Animal Farm. He is frequently inebriated. He is cruel to animals who are hungry. He stands in for Tsar Nicholas II, who was deposed by the Revolution.

Therefore, option D is correct.

Learn more about reckless here:

brainly.com/question/28618592

#SPJ7

This natural resource was once very abundant in Western Europe and helped power the Industrial Revolution. Question 4 options: Iron Coal Oil Water.

Answers

Answer: Its Coal

Explanation: I did the K12 quiz

What must be the value of x so that lines c and d are parallel lines cut by transversal p? 12 18 81 99.

Answers

Answer:18

Explanation:

The lines c and d are parallel if x = 18.

Hence, option B is correct.

Use the concept of an equation of line defined as:

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

In the figure,

The corresponding angles are (3x + 45)° and 81°

The objective is to find the value such that lines c and d become parallel.

Since we know that,

The sum of angles of parallel lines passing through a common line is 180°,

Therefore,

(3x + 45)° + 81° = 180°

Simplifying like terms,

3x = 54

Divide both sides by 3,

x = 18

Hence,

The required value of x is 18 which is option B.

To learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ7

The complete question is:

What must be the value of x so that lines c and d are parallel lines cut by transversal p?

A. 12

B. 18

C. 81

D. 99

Emily, an 11-year-old girl, wants to sign-up for a fashion newsletter and sweepstakes. In order to do so, the website wants to know emily's name, address, phone number, and email address. Which of the following is correct?.

Answers

Answer:

Emily must have permission from her parents in order to furnish the information to the website.

Explanation:

She's underaged

What is one of the biggest challenges when companies are committed to sustainability brainly.

Answers

There are lots of challenges when it comes to keeping up with sustainability.  One of the biggest challenges when companies are committed to sustainability is that the surrounding community needs to understand the environmental impact of the changes.

Sustainable development and climate action are said to have some linkages and both are very important to the present and future health of humanity.

Some of the challenges in corporate sustainability is that there is also a mental shift  so as to consider sustainability in all aspects of the business.

 Learn more from

https://brainly.com/question/16847935

Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Predictable) Education investment fund $10 Other (Predictable) Retirement investment fund $40 Other (Predictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings? a. $40 b. $60 c. $74 d. $55.

Answers

Answer:

C. 74

Explanation:

Answer:

Explanation:

C 74

Read this sentence from an informative essay. After the Civil War, the amount of counterfeit money in circulation was a big problem for the government. The sources for this fact are an article entitled "Know Your Money" from the US Secret Service website and an encyclopedia article entitled "United States Secret Service" by Michael Ray. How should the sources be listed in a parenthetical citation? (Know Your Money; Ray) (US Secret Service; Michael Ray) (Know Your Money; United States Secret Service) ("Know Your Money," US Secret Service; Michael Ray, "United States Secret Service").

Answers

Answer:(know your money ray )

Explanation:

I just took the test on edg good luck

The sources should be listed in a parenthetical citation as: A. (Know Your Money; Ray).

What is a parenthetical citation?

A parenthetical citation can be defined as a type of citation that is used as a reference of the original sources used in a literary work, so as to immediately inform readers where the data were obtained from.

In this scenario, we can infer and logically deduce that the sources should be listed in a parenthetical citation as (Know Your Money; Ray).

Read more on parenthetical citation here: https://brainly.com/question/1260394

#SPJ9

Hydrogen and nitrogen combine to form ammonia. When nitrogen and hydrogen bond, nitrogen pulls the electrons from hydrogen toward itself. Which statement about the reactants is correct?.

Answers

Answer:

Nitrogen is more electronegative, so it pulls the electrons in the bond closer to itself

Explanation:

no statements given

why did the mushroom go to the party

Answers

uh I don't know why? tell me im really clueless

Because he's a fungi

What is the ratio of the area of ABC to the area of ABD? A. B. C. D.

Answers

Answer:

Explanation:

area ABD = 16*12/2  

area ABC = 9*12/2

------------------------------

so the ratio of the area ABC to the area of ABD = (9*12/2)/(16*12/2) =  

= 9/16  

hope this helped!

mark me brainliest :D

The ratio of the area of ABC to the area of ABD is 9/16. The correct option is B.

What is the area?

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

The area of a triangle is the region bounded by its perimeter or its three sides. The area of a triangle can be calculated using the formula, where the base of the triangle is b and the height is h.

A = ½ (b × h)

The two areas will be calculated as:-

Area ABD = ( 1 / 2 )  x 16  x  12

Area ABC = (1 / 2 ) x  9  x  12

So the ratio of the area ABC to the area of ABD will be

= [ ( 1 / 2)  x 16  x  12 ]  ÷  [ (1 / 2 ) x  9  x  12 ]

=  9 / 16

Therefore, the area of ABC to the area of ABD is 9/16. The correct option is B.

To learn more about the area, refer to the below link:

brainly.com/question/25292087

#SPJ5

The question is incomplete. Your most probably complete question is given below:

A. 6/12

B. 9/16

C. 8/16

D. 7/8

Global competition accelerated product development by competitors.

Answers

Answer:

its b

Explanation:

Brent is a 22-year-old man who doesn't smoke. His rda for vitamin c is 90 mg per day. If he takes ______ mg of vitamin c each day, he will consume megadose amounts of the vitamin. (check all that apply. ).

Answers

the answer should be 900 - 1000

Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19. 6 meters. The lengths of J N and N L are 7. 4 meters. The lengths of K M and M L are 10. 7 meters. What is the distance between points M and N? meters.

Answers

Answer:

9.8

Explanation:

just did assignment

How many moles are represented by 12. 33 g of carbon dioxide?.

Answers

Explanation:

formula:

mass - moles = mass given ÷ molar mass

R.M.M of CO2 = 32 + 6 = 38

Molar mass of CO 2 = 38g (recall that r.m.m = molar mass)

38g of CO2 will produce 1 mole

therefore 12.33g will produce:

12.33÷38g (recall formula above)

answer: 0.324 moles

What are the victims of the Guerra Sucia called? "victimones" "The Bad Ones" "The Disappeared" "Unlucky Few".

Answers

The disappeared is a term used for people who are missing. The victims of the Guerra Sucia called The Disappeared

Desaparecidos as it is popularly called is a name synonymous to South America. It simply means when an individual is not seen anymore, and most times presumed dead or killed anyone.

This world is used mostly by Latin America to imply that a particular person has been secretly imprisoned or killed during a government's vendetta of political suppression.

Learn more from

https://brainly.com/question/16117964

Answer:

"The Disappeared"

Explanation:

Which element is reduced in the following reaction? cu + 2h2so4 → cuso4 + so2 + 2h2o.

Answers

Answer:

2h6t

Explanation:

Problems with sleep are more common than sleep disorders or parasomnias. Please select the best answer from the choices provided T F.

Answers

Answer:

True

Explanation:

E2023

Answer:

true

Explanation:

Other Questions
what would this one be? Choose the correct form of of the passcompos3.mon sac main et le porte-monnaie tait l'intrieur.-a perdue-as perdus-ai perdu4. La sculpture grecqueles sculpteurs utilisent cette techniqueactuellement.-n'a pas disparu- n'ai pas disparu-n'a pas disparue5. Les architectesun nouveau stade pour les Jeux Olympiques.-Ont construits-ont construit-Ont construites A fruit basket contains oranges and grapefruits. 1/3 of oranges and 1/4 of the grapefruits were spoiled. You threw away 4 oranges and 7 grapefruits. How many pieces of fruit were in the basket before you threw out the spoiled ones? what is 7/8 as a decimal rounded to the nearest thousandth president lincoln favored a strategy that focused on capturing and holding confederate territorynamely richmond, the confederate capitalnot the destruction of the confederate armies. Which of the following structures of the respiratory system helps to prevent choking? foetus grows by receiving nutriens and oxygen from the mother. How does the foetus receive these nutriens and oxygen? FIND THE MISTAKE IN THIS SENTENCE: (..) I really wish I (would have) a car of my own so that I (could go) for a drive in the country and I (would be able) to go when I want to and not (have to) wait for a bus or a train. where did ahmaud arbery live in relation to where he was killed which of the following has factor of ( - 4) ( - 3)? Please help and give real answers it would be much appreciated Is "quiero comer mi manzana en el patio" grammatically correct 4) 4+ 1 =a) 5b) 57212c) 51d) 572612 please i need help How many rows of seats are inside the theater? Enter your answer in the box. a quorum of _ justices need to be present in order to conduct business.a. 5b. 6c. 8d. 9 Which items are on both the balance sheet and the statement of owner's equity?Question 17 options:CapitalAdditional owner's investmentsNet lossOwner's withdrawals If Celia has been sentenced to 2 years in prison, what type of crime was she most likely convicted of The contestants receiving the fewest viewersvotes are ______from the competition. An extended period of below-average precipitation caused by changes in wind directions, weather patterns, or ocean currents is called which of the following changes will result in a weaker electromagnet