Define the function
3
g(x) = x^3+ x
. If
f(x) = g^-1(x)
and
f(2) = 1
what is the value of
f'(2)
?

Answers

Answer 1

Given that

[tex]g(x) = x^3 + x[/tex]

the inverse [tex]g^{-1}(x)[/tex] is such that

[tex]g\left(g^{-1}(x)\right) = g^{-1}(x)^3 + g^{-1}(x) = x[/tex]

or

[tex]g\left(f(x)\right) = f(x)^3 + f(x) = x[/tex]

Differentiating both sides using the chain rule gives

[tex]3f(x)^2f'(x) + f'(x) = 1 \\\\ f'(x) \left(3f(x)^2+1\right) = 1 \\\\ f'(x) = \dfrac1{3f(x)^2+1}[/tex]

Then the derivative of f at 2 is

[tex]f'(2) = \dfrac1{3f(2)^2+1} = \boxed{\dfrac14}[/tex]


Related Questions

Arrange these numbers in order from least to greatest.​

Answers

Answer:

1) 0.725.

2) 7/25.

3) 7.5%.

(9+8i)(5-5i) in standard form

Answers



The correct answer hope this helps and Brainliest?

(9+5i)(9+8i)
81+72i + 45i -40
41+ 117i

Answer:

40i²-5i+45

Step-by-step explanation:

(9+8i)(5-5i)9(5-5i)+8i(5-5i)45-45i+40i-40i²45-5i-40i²40i²-5i+45

Solve for Rational Inequality.

(x+3)(X+5)x+2≥0

Answers

Do you want me to graph it

he total cost of 5 doughnuts and 6 cookies at a bakery is $11.95. The cost of each cookie is $0.95.



Select the equation and its solution that can be used to determine the cost, x, of 1 doughnut.

Answers

Answer:

x=1.25

Step-by-step explanation:

Answer:

($0.95 * 6) + (5x) = $11.95

The cost of one donut (x) = $1.25

Step-by-step explanation:

I hope this helps!

What is 9(-7)?
I don't even know this

Answers

-63. Hope this helps!

Can have brainliest?

Answer:

-63

Step-by-step explanation:

If you know how to multiply it without the negative then you could take that answer and then put a negative at the beginning.

berapakah hasil dari 33 1/2 - 7 x 8 + 2 - 5,5 adalah, mohon bantuan nya kakak

Answers

Saya yakin jawabannya adalah -26 karena ketika Anda melakukan perkalian terlebih dahulu, kemudian lakukan pecahan 33 1/2 dan setelah itu Anda akan menambahkan 2 dan pengurangan 5,5 yang semuanya akan sama dengan -26. semoga saya benar dan ini membantu. (:

Help me plz o don’t know what to write and how to plz help me

Answers

9514 1404 393

Explanation:

Anything is categorized by how it matches with the definition of the category.

A composite number is a product of primes. A prime number is divisible only by itself and 1.

If a number has more than one prime factor (even if that is just multiple instances of the same prime factor), it goes into the composite number category. If its only prime factor is itself, it goes into the prime number category.

What is the value of 9 squard

Answers

I presume you mean 9 'square'

9^2= 9 X 9 = 81

Cheerio ✌️

Step-by-step explanation:

The value of 9 Square is = 9 ×9= 81

Hope it's help you

Write the measure in degrees (pi)/4

Answers

Let's see

[tex]\\ \rm\longmapsto \pi/4[/tex]

[tex]\\ \rm\longmapsto \dfrac{\pi}{4}\times \dfrac{180}{\pi}[/tex]

[tex]\\ \rm\longmapsto \dfrac{180}{4}[/tex]

[tex]\\ \rm\longmapsto 45°[/tex]

The solution is: the measure in degrees (pi)/4 is 45°.

Here, we have,

given that,

we have to find  the measure in degrees (pi)/4.

now, we know that,

Measure of an Angle in Degrees = 180°        

Measure of an Angle in Radians is:

180° × (π/180°) = π = 3.14 Rad

so, we have,

π/4

= π/4 × (180°/π)

=180 /4

=45°

Hence, the measure in degrees (pi)/4 is 45°.

To learn more on angle click:

brainly.com/question/28451077

#SPJ6


2.5% of 2 2/5
is what number?

Answers

Answer:

The number is 0.06, or 6 hundredths.

Step-by-step explanation:

If we convert 2 2/5 to a decimal, we get 2.4

Then, we can convert our percentage to a decimal by moving our digits two units down, giving us .025.

Now, we can multiply 2.4 and .025, which gives us 0.06

13) Store A and Store B both sell apples by the pound. Store A uses the function y = 0.38x,
where y represents the total cost in dollars and x represents the number of pounds. The
relationship between weight and cost at Store B is shown in the table. At which store
are apples more expensive?
50 Points NEED HELP ASAP PLS AND THANK YOU

Answers

A) Store A

B) Store B

C) The cost is the same at both stores

C is the answer

3 out of 100 is what percentage?

A 3%
B 30%
C 18%
D 100%

Answers

Answer:A 3%

Step-by-step explanation:

The total temperature measured by 3 thermometers was −15 degrees Fahrenheit.

What was the average temperature measured by the 3 thermometers?

Answers

Answer:

-15 ÷ 3 = -5

Step-by-step explanation:

If 3 thermometers totaled -15, then they share that value equally.

find the y-intercept of the parabola y=x^2-5x+9/2

Answers

Answer:

To find the Y-intercept substitute in 0 for all the x's and solve for Y

Your answer would be (0,9/2)

Steps:

Y=0^2-5(0)+9/2

0^2 -5(0)=0

Y=9/2

0 is your x place

and 9/2 is your Y intercept

Answer:

y-intercept = 9/2 or 4.5

Step-by-step explanation:

In the given quadratic equation, y = x² - 5x + 9/2, where:

a = 1, b = -5, and c = 9/2  

The y-intercept is the point at which the parabola crosses the y-axis, and occurs at point (0, c ).  It is the value of y when x = 0. To find out what I mean by this, we can substitute the value of x = 0 into the quadratic equation:

y = x² - 5x + 9/2

y = (0)² - 5(0) + 9/2

y = 0 - 0 + 9/2

y = 9/2

Therefore, the y-intercept (c) = 9/2, and has coordinates, (0, 9/2) or (0, 4.5).

Attached is a screenshot of the graph, where it shows the y-intercept.  

Please mark my answers as the Brainliest, if you find my explanations helpful :)

find the value of x and y
will give brainiest

Answers

Answer:

[tex]2x + 7 = 3x - 7 \\ 3x - 2x = 7 + 7 = 14 \\ x = 14 \\ 2x + 7 + 12y + 1 = 180 \\ 12y + 36 = 180 \\ 12y = 180 - 36 = 144 \\ y = 144 \div 12 = 12[/tex]

A soccor team last 30% of its games suppose the team won 14 games how many games did the team play

Answers

Answer:

its 20 games in total

the equation is 14×100÷70

Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
-5x + y = -2
20x – 4y = 8

Answers

This are similar answers to your questions.

each face of a cube is a square with a side length of 7 inches what is the total area off all the faces of the cube

Answers

Answer: 294 square inches

Explanation:
A = L*W
In a square, all side lengths are equal.
A = 7*7
A = 49 square inches
^^^this is the area of one face of the cube

A cube has six faces, so multiply that value by 6.
49 * 6 = 294 square inches

Write an equation of the line in slope intercept form for (0,3) and (4,2)

Answers

Answer: 13

Step-by-step explanation:

Step-by-step explanation:

the slope is the y/x ratio of the y and x coordinate differences when going from one point to the other. and it is always the factor of x in the equation.

x changes by 4 units (from 0 to 4), y changes by -1 unit (from 3 to 2).

so, the slope is -1/4.

the intercept means the intercept with the y-axis. and that means the y value when x = 0. which is given already by the first point : 3

so, the equation is

y = -1/4 x + 3

expression is equivalent to (f + g)(4)

Answers

Answer:

Answer: The Expression (f + g)(4) is equal to f(4) + g(4).

Step-by-step explanation:

The probability of drawing three spades in a from from a standard deck of cards when the drawn card is returned to the deck each time.

Answers

Answer:

1/64

Step-by-step explanation:

P(pick 3 consecutive spades with replacement of drawn cards) =

(13/52)(13/52)(13/52) =

(1/4)(1/4)(1/4) =

1/64

Overdraft protection can be set up to which of the following accounts?

a. Savings account
b. Credit Card
c. A line of credit
d. All of the above

Answers

The answer would be all the above

What is the equation of the line that passes through the point (–2, 1) and
has a slope of - 5/2

Answers

Answer:

y = -5/2x + -4 (or) y = -5/2x - 4

Step-by-step explanation:

Your slope is -5/2, so all you have to do is take the point (-2, 1) and use the slope to find a second point of (0, -4) which is coincidentally the y-intercept. Then you just plug the data into the equation y = mx+b. You do that and you get the answer of y = -5/2x+-4


help! will mark branliest

Answers

Answer:

B is the answer hope you get it right

need help asap on 9, 10,and 11

Answers

Step-by-step explanation:

9. a)

2•(-2) = 2 - 6

-4 = -4

-2 -2 = -2•2

-4 = -4

Yes, the ordered pair is the solution

9. b)

-1 = 3•(-2) +5

-1 = -6 +5

-1 = -1

3•(-2) +(-1) = -2

-6 -1 = -2

-7 ≠ -2

No, the ordered pair is not the solution

10. (-1, -1) and (3, -1)

11.

y = 6 +x

Now substitute it in the first equation:

3•(6 +x) = 5x

18 + 3x = 5x

18 = 2x

x = 18/2

x = 9

Now, substitute x = 9 in the second equation:

y -9 = 6

y = 6 +9

y = 15

The entire graph of the function f is shown in the figure below.
Write the domain and range of f using interval notation.

Answers

Answer:

range =[-5,5]

domain =[-2,3]

Select all of the equations that are equivalent to 3 x − 12 = 19
A 3x-12=19
B 3x=7
C 3x=31
D 3x+31=0
E 5x-12=2x+19
F x-4=(19/3)

Answers

Answer:

X=2

Step-by-step explanation:

x

=

2

Explanation:

Collect terms in x on the left side of the equation and numeric values on the right side.

add 3x to both sides.

5

x

+

3

x

+

12

=

3

x

+

3

x

4

8

x

+

12

=

4

subtract 12 from both sides.

8

x

+

12

12

=

4

12

8

x

=

16

To solve for x, divide both sides by 8

8

x

8

=

16

8

x

=

2

As a check

Substitute this value into the equation and if the left side is equal to the right side for this value then it is the solution.

left side  

=

(

5

×

2

)

+

12

=

10

+

12

=

2

right side  

=

(

3

×

2

)

4

=

=

6

4

=

2

x

=

2

is the solution

Answer:

b Beacuse you can't times 3 by twelve but you can multiple 3times7+1 to get 19

Pls help ASAP pls it’s reasoning with fractions

Answers

84 decimetres is the answer!

I will mark brainlist please help!!

- dilation (lesson)

1) in a dilation of a figure, the distance between two consecutive vertices does not change

• true

• false


2) the coordinates of the vertices of a triangle JKL are J (4,8) K (8,8) L (4,2). Find the coordinates of the vertices of the image after a dilation by K = 0.25


• J (2,1) K (2,2) L (1,2)

• J (-2,1) K (4,2) L (1,0.5)

• J (1,2) K (2,2) L (1,0.5)

Answers

Answer:

see explanation

Step-by-step explanation:

(1) False

A dilatation enlarges or reduces the original figure

Then the distance between consecutive vertices changes.

(2)

Assuming the centre of dilatation is at the origin then multiply the coordinates of the points by the scale factor k = 0.25 ( a reduction )

J (4, 8 ) → J' (4(0.25), 8(0.25) ) → J' (1, 2 )

K (8, 8 ) → K' (8(0.25), 8(0.25) ) → K' (2, 2 )

L (4, 2 ) → L' (4(0.25), 2(0.25) ) → L' (1, 0.5 )

NEEED HELP ASAP PLS.................

Answers

(6)(-2)= 12
(-6)(2)= -12
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