Let f be the function defined by f(x)=x^3+x^2+x. Let g(x)=f^-1(x), where g(3)=1. What is the value of g'(3)?

Answers

Answer 1

Answer:

1/6

Step-by-step explanation:

Given the function

f(x)=x^3+x^2+x

Get the inverse. Let y = f(x)

y = x^3+x^2+x

Replace y with x

x = y³+y²+y

Differentiate with respect to x

1 =3y²dy/dx + 2ydy/dx + dy/dx

1 = (3y²+2y+1)dy/dx

dy/dx = 1/3y²+2y+1

g'(x) = 1/3(g(x))²+2g(x)+1

If x = 3

g'(3) = 1/3(g(3))²+2g(3)+1

g'(3) =1/3(1)²+2(1)+1

g'(3) = 1/3+2+1

g'(3) = 1/6

Hence g'(3) = 1/6


Related Questions

Help me please...........

Answers

Answer:

6/19

Step-by-step explanation:

Answer:

6/19 subtracting 3 each time form the numerator

Step-by-step explanation:

Is this a function?

Answers

i think it is!

there are no points that are in the same x unit!

hope this help! :(

Find f (-12) if f (x) = -12x + 100​

Answers

f(-12) = -12(-12) + 100 = 144 + 100 = 244

Answer:

244

Step-by-step explanation:

Substitute -12 as x.

f (-12) = -12(-12) + 100

f (-12) = 144 + 100

f (-12) = 244

I hope this helped! :)

1) someone help easy math question

Answers

Answer is -9 it’s easy

73 minus what plus 24 equals 73

Answers

Answer:

24

Step-by-step explanation:

Which ordered pair is the solution to this system of equations?
2x - y = 10
x+y=2
A) (4,-2)
B) (4,2)
C) (2,-4)
D) (-4,2)

Answers

Answer:

A) (4, -2)

Step-by-step explanation:

please help me (see picture)

Answers

Answer:

107 degrees

Step-by-step explanation:

to find x = 180 - (180-73-34)

x = 180 - 73

x = 107

What is the greatest common factor of 42 and 50?

Answers

Answer:

2 is the gcf of 42 and 50

The greatest common factor of 42 and 50 is: 2

How to find the Greatest common factor?

The greatest common factor, the name implies, is the greatest among all common factors among the quantities.

We have to factorize the quantities in the smallest relative factors possible (one level of factors over which all quantities can form themselves) and collect as many common factors as we could.

Those will together compose GCF.

Take out the factors of the numbers given:

42: 1, 2, 3, 6, 7, 14, 21, 42

50: 1, 2, 5, 10, 25, 50

The common numbers between the two are 1 and 2, but the greatest number is 2, which becomes the greatest common factor.

Learn more about the greatest common factor here:

https://brainly.com/question/207329

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i’m stuck with these questions

Answers

Answer:

Step-by-step explanation:

3) using the property of opposite angles we can work out that HFJ=138

Its that simple. if two lines intersect, the angles on either side are the same

4)I don't know how to find segments of circles...

Step-by-step explanation:

option A 138 °option D 320°option 300°

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you

WILLL GIVE BRAINIEST!!!!!

Answers

x = 1/5Y

I hope this helped! please mark brainliest and vote 5 stars >:)

which of the following equations is equivalent to 100x - 90 - x + 25 = 30?

Answers

Answer:

99x-65=30

Step-by-step explanation:

Cameron is 5 ft tall and casts a 12 ft shadow. At the same time of day, a nearby
building casts a 78 ft shadow. How tall is the building? Hint: Make a sketch and label all
measurements first.

Answers

Answer:

the building would be 32.5 feet tall.

Step-by-step explanation:

Mitch puts $500.00 into an account to use for school expenses. The account earns 12% interest,
compounded annually. How much will be in the account after 8 years? Round your answer to
the nearest cent.

pls hurry it’s for a math test

Answers

Answer:

there will be 20 dollars

Step-by-step explanation:

500 multiplied by .12 and then timesed by 8 then subtracted by 500

hey can someone help:)?​

Answers

I think it’s the first one

umm helpppppppppppppp

Answers

Answer:

Step-by-step explanation:

y= 2x +1 because

11= 2*5 +1

13 = 2*6 +1

21= 2*10 +1

so for x=8 will be n= 2*8+1 = 17

Linear Equations Digital Escape! Can you find the slope-intercept equation of each line and type the correct code?

Answers

Answer: I can if there’s a picture...

Step-by-step explanation:

Answer: cgia

Step-by-step explanation:

Given f(x) = 2 sin x, find the exact value of f (7pi/6) in simplest form with a rational denominator.​

Answers

Answer:

           [tex]\bold{f(\frac{7\pi}6)=-1}[/tex]

Step-by-step explanation:

[tex]f(\frac{7\pi}6)=2\sin(\frac{7\pi}6)=2\sin(\frac{7\pi}6)=2\sin(\pi+\frac{\pi}6)=-2\sin(\frac{\pi}6)=-2\cdot\frac12=-1[/tex]

What is the eqution of the following line?
y=4x−1
y=4x+4
y=−4x+4
y=−4x−1

Answers

y= 4x+4
hope this helps :)

Elena and jada are going home. Elena runs at a constant speed of 4 miles per hour, and jada walks at a constant speed of 2 miles per hour. How far will each one be after 1.5
hours

Answers

Answer:

Elena will run 6 miles in 1.5 hours

Jada will walk 3 miles in 1.5 hours

Step-by-step explanation:

Multiply: 4*1.5=6 (Elena's)

Multiply:2*1.5=3  (Jada's)

Elena will run 6 miles in 1.5 hours

Jada will walk 3 miles in 1.5 hours

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

Please correct me if I'm wrong

A line passes through the point (-8, – 4) and has a slope of 5/4 write an equation in point slope form

Answers

y=5/4x+6 is in slope intercept form I forgot how to do point slope

The graph of 3x - 5y = 12 is shown on the grid. Which ordered pair is in the solution set of 3x - 5y 2 12? es ) A) (0,5) B) (5,0) © (-3,5) D) (-5,3)​

Answers

Answer:

i think itz C

Step-by-step explanation:

The required ordered pair is (5,0) in the solution set of the given inequality 3x - 5y ≥ 12. The correct answer would be option (B).

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The given graph of 3x - 5y = 12 is shown on the grid.

To find the solution set of 3x - 5y ≥ 12, we need to shade the region of line 3x - 5y = 12 since it represents all the points that make the inequality true.

When all the given points are drawn in the graph, then we get the ordered pair (5,0) in the solution set of the given inequality.

Thus, the required ordered pair is (5,0) in the solution set of the given inequality 3x - 5y ≥ 12.

Therefore, the correct answer would be an option (B).

Learn more about inequalities here :

brainly.com/question/20383699

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help Find value of ST, Geometry problem

Answers

13 because the scale factor is 1/3

Answer:

It would be 13.

Step-by-step explanation:

if line f passes through points (9 , 9) and (6 , 1) . Line g is perpendicular to line f. What is the slope of line g?

Answers

I have no clue but I’m sure someone on here will send you in the right path. Sorry and good luck

PLEASE HELP, I CANT FIGURE IT OUT AND IT IS DUE TOMORROW MORNING
Find area of the isosceles triangle formed by the vertex and the x-intercepts of parabola y=−x^2−4x+21.

Answers

Answer:

Xmin: -10

Xmax: 10

Ymin: -10

Ymax: 10

The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks plus $250 for each ton of sugar
transported. The total cost, C (in dollars), for transporting n tons is given by the following.
C = 3500+ 250n

What is the total cost of transporting 15 tons?

In the total cost is $8750, how many tons is the company transporting?

Answers

Answer:  Equation relating C to S   :

The total cost to transport 19 tons of sugar is $11, 250.

Step-by-step explanation:

Given : It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported.

Total cost =  $6500 + $250 x (amount of sugar transported ( in tons))

Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported.

Then, the equation relating C to S  would be :

When S= 19 , we get

Hence, the total cost to transport 19 tons of sugar would be $11, 250.

HUrRiCAn KatrINa?? MORe liKE?

Answers

Answer:

Step-by-step explanation:

HUrRiCAn PepiNa

19% of £394.22. Give your answer rounded to 2 DP.
Someone please quickly respond back! Thanks.

Answers

Answer:

3

Step-by-step explanation:

if you round it by the nearest 2 you get 3

a) Find the value of 8 1/3
b) Find the value of 8 2/3
c) Find the value of 16 3/4

Answers

hope it's helpful ❤❤❤❤❤❤

THANK YOU.

#

Answer:

2, 4 and 8

Step-by-step explanation:

Using the rule of exponents/ radicals

[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex]

(a)

[tex]8^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{8}[/tex] = 2

(b)

[tex]8^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{8^{2} }[/tex] = 2² = 4

(c)

[tex]16^{\frac{3}{4} }[/tex] = [tex]\sqrt[4]{16^{3} }[/tex] = 2³ = 8

A rectangular poster is 2/3 meter long and 1/2 meter wide. What is the area of the poster in fraction form

Answers

Answer:

1/3

Step-by-step explanation:

pleaze help the question is in the picture

Answers

45+x is your answer

Answer:

A because we need the amount of time she played soccer for so we need to add the 2 days together

Step-by-step explanation:

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