If f and h are inverses of one another, then we have
h(f(x)) = x
Differentiating both sides using the chain rule gives
h'(f(x)) • f'(x) = 1
Let f(x) = -1. Then it would follow that
h'(-1) = 1/f'(x)
for the value of x such that f(x) = -1. This result is known as the inverse function theorem.
Solve for x such that f(x) = -1 :
2x³ - 3x = -1
2x³ - 3x + 1 = 0
By inspection, x = 1 is a solution, since 2 - 3 + 1 = 0. So x - 1 is a factor of the left side; polynomial division yields a factorization of
(x - 1) (2x² + 2x - 1) = 0
and using the quadratic formula, we find three solutions,
x = 1, x = (-1 - √3)/2, x = (-1 + √3)/2
Since there's more than one solution here, this means f(x) is not one-to-one and thus has no inverse in the strict sense of the term.
We can however restrict the domain of f(x) to a subset over which it can be inverted. Using the fact that polynomials are monotonic over intervals between their extrema, we find the critical points of f(x) :
f'(x) = 6x² - 3 = 0 ⇒ x² = 1/2 ⇒ x = ± 1/√2
Check the sign of the second derivative at each critical point:
f''(x) = 12x
• f''(-1/√2) = -12/√2 < 0 ⇒ x = -1/√2 is a local maximum
• f''(1/√2) = 12/√2 > 0 ⇒ x = 1/√2 is a local minimum
Now we have a few choices of how to define the inverse of f(x).
• If we restrict the domain of f(x) to the interval (-∞, -1/√2), then f(x) = -1 when x = (-1 - √3)/2. Then by the inverse function theorem,
f((-1 - √3)/2) = -1 ⇒ h'(-1) = 1/f'((-1 - √3)/2) = (-1 + √3)/6
• If we instead restrict the domain to (-1/√2, 1/√2), then f(x) = -1 when x = (-1 + √3)/2. Then
f((-1 + √3)/2) = -1 ⇒ h'(-1) = 1/f'((-1 + √3)/2) = (-1 - √3)/6
• Otherwise, if we restrict to (1/√2, ∞), then f(x) = -1 when x = 1. Then
f(1) = -1 ⇒ h'(-1) = 1/f'(1) = 1/3
List the molecules of the “energy investment phase” in order starting from Glucose?
Answer:
Energy investment phase. Glucose is first converted to fructose-1,6-bisphosphate in a series of steps that use up two ATP. Then, unstable fructose-1,6-bisphosphate splits in two, forming two three-carbon molecules called DHAP and glyceraldehyde-3-phosphae.
Explanation:
hope it helps you
5.During the process of condensation water in ________ state changes to ________ state.
Larousse Language College will have 201 students in the Sixth Form next year. Mr Roche, who
does the timetabling, knows that between 70% and 75% of the students intend to study French
and between 40% and 50% of the students intend to study German. All students study either
French or German or both.
By using Venn diagram method, the smallest and the largest number of students that intend to study both French and German are 21 and 49 students respectively.
Given that Larousse Language College will have 201 students in the Sixth Form next year. And between 70% and 75% of the students intend to study French. Also, between 40% and 50% of the students intend to study German.
If all students study either French or German or both, the least number of students that will study French will be
70/100 x 201
140. 7
Which means 141 students
The least number of students that will study German will be
40/100 x 201
80.4
That means 81 students
Also, the maximum number of students that will study French will be
75/100 x 201
150.75
That is 150 students ( Because approximation can't be done twice)
And the maximum number of students that will study German will be
50/100 x 201
100 students ( Because approximation can't be done twice)
a.) The smallest number of students that intend to study both French and German can be calculated as followed
Let the smallest number be x
141 - x + x + 81 - x = 201
222 - x = 201
- x = 201 - 222
-x = - 21
x = 21
b.) The largest number of students that intend to study both French and German can be calculated as followed
Let the largest number be y
150 - y + y + 100 - y = 201
250 - y = 201
- y = 201 - 250
-y = - 49
y = 49
Therefore, The smallest and the largest number of students that intend to study both French and German are 21 and 49 students respectively.
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Use the FOIL method to find the terms of the following multiplication problem.
(4+3i) (6-3i)
Answer:
FOIL = First terms, outer terms, inner terms, and last terms. The product of the first terms is 24 (4*6). The product of the outer terms is -12i(4*-3i). The product of the inner terms is 18i(3i*6). The product of the last terms is -9i^2(3i*-3i). "i^2"= -1 So, -9*-1= 9.
In a cluster sample:
A. a subset of naturally occurring groups are randomly sampled.
B. an alphabetic list of individuals is used for random selection into
the sample.
C. individuals are distinguished based on some characteristic such
as gender before they're randomly selected from the population.
D. only convenient members of the population are chosen.
E. None of the above
In a cluster sample only convenient members of the population are chosen. The correct option is D.
What is cluster?In cluster sampling, a population is divided into clusters, which are smaller groups. They then choose a sample at random from these clusters.
Often employed to investigate huge populations, particularly those that are extensively geographically distributed, cluster sampling is a probability sampling technique.
Large, dispersed populations should be studied using cluster sampling because interviewing every individual would be expensive, time-consuming, and possibly impossible.
Cluster sampling enables the construction of smaller, more similar representations of the population being studied. Only practical population members are picked for a cluster sample.
Thus, the correct option is D.
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John notices Jimmy taking $5 from the cash register at the end of the night. Jimmy says that the company owes him for making him work three Friday nights in a row. Jimmy also asks John not to tell anyone. John’s ethical duty is to ______. a. Stay loyal to Jimmy and not turn him in b. Forget the incident because it doesn’t involve him c. Ask Jimmy for half the money not to tell d. Turn Jimmy in despite his protests Please select the best answer from the choices provided A B C D
Answer:
Explanation:
super subjective, but i assume they want D
John’s ethical duty is to turn Jimmy in despite his protests, hence option D is correct.
What is work Ethics?Work Ethics are a set of standards, values, and moral with which employees executes their duties e,g Integrity.
In this case, if John does not turn Jimmy in, he will be an accomplice which is unethical also.
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Read the following poem carefully before you choose your answer.
The following poem is addressed to a friend of the speaker.
Then hate me when thou wilt; if ever, now;
Now, while the world is bent my deeds to cross,
Join with the spite of fortune, make me bow,
And do not drop in for an after-loss:
(5) Ah, do not, when my heart has 'scaped this sorrow,
Come in the rearward of a conquered woe;
Give not a windy night a rainy morrow,
To linger out a purposed overthrow.
If thou wilt leave me, do not leave me last,
(10) When other petty griefs have done their spite;
But in the onset come, so shall I taste
At first the very worst of fortune's might;
And other strains of woe, which now seem woe,
Compared with loss of thee, will not seem so.
(1609)
Which of the following best describes the function of the poem's couplet?
A) It challenges the notion that the relationship will end.
B) It discounts the speaker's concerns with a hint of possible change.
C) It introduces an explanation for the speaker's strong feelings.
D) It remarks on the recipient's sudden and unexpected change of heart.
E) It summarizes why the relationship should be dissolved now.
Answer:
b is the answer if not sorry
The poet's couplet describes the It discounts the speaker's concerns with a hint of possible change.
What is fortune's night?This particular sonnet and those which are numbered 1-126 belong to Shakespeare’s famous Fair Youth sequence. These poems are devoted to a young, beautiful man whose identity remains unknown to this day. There has been a great deal of speculation about who this young man could possibly be, but no single identity has ever been decided upon.
Shakespeare uses a variety of poetic devices in "Sonnet 90." These include metaphor, caesura, and alliteration, among others. When words that start with the same sound are used consecutively or even just near to one another, alliteration develops.
When a line is cut in two, sometimes with punctuation and other times without, this is known as a caesura. Punctuation in these places causes a highly deliberate stop in the text.
Therefore, The poet's couplet describes the It discounts the speaker's concerns with a hint of possible change.
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how do i find the limiting reactant
The Image demonstrates the legacy of:
a nation-state
federalism
separatism
colonialism
dependency theory
Answer:
federalism
Explanation:
the Parliament is the federal institution with the power to make laws, to raise taxes, and to authorize government spending.
20 POINTS!!!!
Which of the following statements BEST describes the position of the United States following World War II?
The United States should set up and control democratic governments in allied European countries.
Promoting democracies in European countries is the best way for the United States to combat the spread of communism.
The United States should not be expected to provide financial aid to countries struggling to rebuild after the war.
It is not the United States' responsibility to provide aid to states that have resisted communist takeovers.
The United States should focus attention on Western Europe only.
What composition of rigid motions maps ΔPQR to ΔXZY?
A. T<1, 3> ◦ r(270°, O)
B. Rx = 0 ◦ T<0, 2>
C. T<6, 2> ◦ Rx = −2
D. Ry = −2 ◦ T<6, 0>
Answer:
reflection across x=1, translation up 2
units
Step-by-step explanation:
The order of vertices PQR is
clockwise, and the order of XZY
is counterclockwise. This means a
reflection is involved. The longest and
shortest sides are at the left and bottom
of APQR, and at the right and bottom
of AXZY, indicating the reflection is
left-right, not up-down.
Line x=1 contains the midpoints of
segments PX, QZ, and RY, so that is a
suitable line of reflection. Once APQR
is reflected over that line, it needs to be
translated upward 2 units to coincide
with AXZY.
The motions are ...
.
reflection over x=1
translation up 2
.
The motions could also be ...
reflection over y, translation right 2 and
up 2.
ANSWER
The composition of rigid motions maps ΔPQR to ΔXZY is T<6, 2> ◦ Rx = −2. The correct option is C.
What are rigid motion maps?In rigid motion, the position or orientation of the entire set changes without affecting the separation between the line segments. A triangle, for instance, can turn or slide but not extend or squeeze.
PQR's vertices are in clockwise and XZY's are in a counterclockwise sequence. This indicates that a reflection is necessary. The reflection is left-right, not up-down, as evidenced by the longest and shortest sides being on the left and bottom of A PQR, and on the right and bottom of AXZY, respectively.
The midpoints of the segments PX, QZ, and RY are on line x=1, making it a viable line of reflection. To match with AXZY, APQR must be translated upward 2 units after crossing that line.
Therefore, the correct option is C. T<6, 2> ◦ Rx = −2.
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The question is incomplete. Your most probably complete question is given below:
The image is added.
Is a type of decision-making who over-analyzes information.
Answer:
Analytical decision-makers carefully analyze data to come up with a solution. They are careful and adaptable thinkers. They will invest time to glean information to form a conclusion.
Explanation:
What are the advantages and disadvantages of two-wheeled transportation?
edge2021
How were social categories, roles, and practices maintained or changed from 1450-1750?
Answer:
This is an essay question. You need to develop a theory about the three biggest forces in world history during that 300 year period. You should look at the movement of capital, the movement of ideas, and the movement of people. That should get you started with a tidy five para structure. You will need to gather some sources together. Happy research!
Which statement is FALSE concerning the Qur'an:
1.
The Qur'an discusses personalities found in Jewish and Christian Bibles
2.
Only the Arabic version is considered to be fully authoritative
3.
Every surah opens, "In the name of God, the Compassionate and Merciful."
4.
Muslims hold up Muhammad's thorough education as a sign of the quality Arabic of the Qur'an
Answer:
Only the Arabic version is considered to be fully authoritative
Explanation:
urgent!
Which of the following becomes
disrupted when we don't feel
self-control?
A. anxiety
B. internal circadian rhythm
C. relational processes
D. personal reality
Self-control could be defined as the conscious ability to regulate impulses voluntarily, if we don't feel self-control relational processes becomes disrupted.
Self-control is the ability to regulate emotions, thoughts and behaviors effectively in different situations.
A person with self-control can manage their emotions and regulate her behavior, copes with setbacks with serenity, has patience and understanding in relational processes.Lack of self-control affects the ability to establish and maintain positive and rewarding relationships with diverse individuals and groups through communication, social commitment, and teamwork.Therefore, we can conclude that self-control allows to regulate emotions, thoughts and behaviors, giving the possibility of choosing actions and reactions to stimuli, with the aim of achieving a greater personal and relational balance.
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Which of the following best explains the changes on the map between 1644 and 1800?
Answer: It incorporated many diverse cultural groups
Explanation:
describe life in the south in 2 sentences
Answer:
Loaded Guns
Explanation:
2 Loaded guns
What holioday is your favorite if you answer correct you get brainliest
100 points
Answer:
Christmas and valentines day
Christmas bc i love giving gifts and spending time with fam
valentines day bc i like getting Chocolate lol
:)
100 Points.
What does it mean when a guy calls you pretty?
I know there is a difference from Pretty Buitiful, and Cute. But I don't know the difference please help.
Answer:
hmm i know STOP BEING A STALKER TO NARUTO
Explanation:
Answer:
Beautiful is probably the highest compliment, because it`s respectful and kinda ego-boosting. When they call you pretty, it`s a lesser version of beautiful but it`s still a nice compliment. Pretty is a term that friends like using amongst each other (at least my friend group, id.k for anyone else).
Cute is just straight up flirtatious, unless you`re talking to a friend. It`s the all-purpose term for complimenting lm.ao
Hope this helps :/
Explain ONE historical situation in the period 1450-1750, other than the one illustrated in the passage, in which states experienced environmental impact.
During the period 1450-1750, are the environmental impact on the soil erosion are the transfer of the diseases.
What is environmental?
The term "environmental" refers to the surrounds on Earth. The environment is made up of both living and non-living entities. The influence of the environment on human life Plants, fisheries, animals, woods, and microorganisms are examples of biotic factors in the environment. Water, land, rocks, air, and other abiotic components are examples.
The movement of cattle and animals from one region to another, notably from the eastern to western hemispheres, had a significant environmental impact in the Americas. The animals brought west overgrazed, causing land degradation and disease transmission.
As a result, during the period 1450-1750, are the environmental impact on the soil erosion are the transfer of the diseases.
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what were georgia's after the proclamation of 1763
Answer:
The Proclamation of 1763 was issued by the British at the end of the French and Indian War to appease Native Americans by checking the encroachment of European settlers on their lands. It created a boundary, known as the proclamation line, separating the British colonies on the Atlantic coast from American Indian lands west of the Appalachian Mountains. In the centuries since the proclamation, it has become one of the cornerstones of Native American law in the United States and Canada.
a crocodile ate my shoes
Answer: Spiderman
Explanation: The raccoon man said so
I am with you wherever you go, but I am never personally there.
What am I????
Answer:
I'm pretty sure the answer is God.
im almost done with high school and I want to go to a college in texas where the love of my life lives. anyone got any suggestions for good colleges there???
Answer:
Trinity University in San Antonio is nice, just know that if you walk around downtown San Antonio (really anywhere in Texas) either carry pepper spray and or other self defense mechanisms and/or walk with a man you trust (that applies only if you are a woman, sadly)
I was there visiting Trinity and it's nice, really nice gyms and stuff, cool food court, other stuff too, but i was walking downtown with MY PARENTS on either side of me and a scary guy came up and cut us off and was making crude comments toward me and was advancing on us. so guys in big cities are bold a-holes.
It seems like going to school in texas would mean out-of-state tuition for you, so apply for any and all scholarships that you can.
Explanation:
What statement is incorrect about natural selection
Answer: What statement is incorrect about natural selection
Explanation: Human genetic modification.
What were some ways that September 11th affected North Carolina’s economy? Check all that apply. It led to several major commercial airline companies relocating to the state. It led to the creation of thousands of military jobs in the state. It led to the opening of more factories across the state. It encouraged more defense and military spending.
Considering the situation described above, some of how September 11th affected North Carolina’s economy include "it led to the creation of thousands of military jobs in the state."
The other way September 11th affected North Carolina’s economy is that "it encouraged more defense and military spending."
September 11, 2001, Terrorist AttackSeptember 11, 2001, Terrorist Attack was an attack on the United States targeting significant buildings such as Pentagon, World Trade Centers, and U.S Capitol.
Following the saddened incident that led to the immediate death of about 3,000 people, its effects were felt across the United States, including North Carolina.
Some of the effects led to increment in the militarization of North Carolina, making the state become the fourth-ranked state with military personnel in the United States with 166,000 troops.
Hence, in this case, it is concluded that the correct answer is options B and D.
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Explain four reasons of preserving farm produce
The following are some of the reasons we preserve our food.
Not to lose it freshness
.To prevent contamination and infection
.To prevent food from smelling
.To keep insect and other pest away from the food.
Keeps farm produce in good condition for planting in the next season
.To keep food for a long period of time.
Explanation:
One- Not to lose it freshness.
Two- To prevent contamination and infection.
Three- To prevent food from smelling.
Four- To keep insect and other pest away from the food.
__________________________________
WHAT IS THAT???
I DON'T UNDERSTAND
What are the benefits that can help the body in doing physical exercise? essay
Answer:
a essay a
Explanation: