Consider the function f(x)=8x3−2. If f(g(x))=x and g(f(x))=x, find g(x)

Answers

Answer 1

I can give you a hint. So when we do the composition of functions, if we plug 2 functions into each other and get x by itself, that means the functions are inversely related.

For this problem, simply find the inverse of f(x).

If you are stuck, I could provide you with a solution below...

f(x) = 8x³ - 2

y = 8x³ - 2

y + 2 = 8x³

(y + 2)/8 = x³

cube root((y + 2)/8) = x

g(x) = cube root((x + 2)/8)

Answer 2

The value of function g(x) after solving will be ∛(x + 2) / 2.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The value of function,

f(x) = 8x³ − 2

And, f(g(x)) = x and g(f(x)) = x

Now,

Since, f(g(x)) = x

And, f(x) = 8x³ − 2

The substitute x = g (x) in above equation we get;

f (g(x)) = 8 (g(x))³ - 2

x = 8 (g(x))³ - 2

Add 2 both side;

x + 2 = 8 (g(x))³  

Divide by 8;

(x + 2)/8 = (g(x))³

Take cube root both side;

∛(x + 2)/8 = g(x)

g(x) = ∛(x + 2) / 2

So, The value of function g(x) after solving will be ∛(x + 2) / 2.

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Related Questions

What numbers round to 200,000 when rounded to the nearest hundred thousand? Select all that apply.

Answers

Answers: Choice C and Choice D

165,400 and 220,574

=================================================

Explanation:

The value in the hundred thousands digit of 165,400 is "1". Just to right of it is "6", which is five or more, meaning we bump that "1" up to "2". Everything else gets replaced with a zero.

The number 165,400 rounds to 200,000 when rounding to the nearest hundred thousand. The number 165,400 is closer to 200,000 than it is to 100,000.

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

In 220,574 we have the first "2" in the  hundred thousands digit with another "2" just to the right of it. Since that second "2" is not five or more, we replace everything with zeros to get 200,000. We won't bump that first "2" up by one.

220,574 is closer to 200,000 than it is to 300,000.

These two sections help show why choices C and D are the answers.

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

Something like 142,026 rounds to 100,000 for similar reasoning as the previous section. So we can rule out choice B.

Choice A rounds to 100,000 as well, so we can rule it out also.

Choice D rounds to 1,000,000 which means we cross it off the list.

What is the median of this data set?
{29, 22, 23, 31, 29, 29, 22, 23}

Answers

Answer:

The median is 26

Step-by-step explanation:

A "median" is equivalent to when the terms are arranged in the proper order, whichever term is in the "middle".

So- first, arrange the terms in ascending order.

[22, 22, 23, 23, 29, 29, 29, 31]

There are an even number- eight- terms in total, so we will take the average of the two "middle" terms.

(29+23)/2; 29 and 23 are the "middle" terms, and there are two of them.

(52)/2 = 26

Therefore, the median is 26.

I hope this helped! :)

Hello!

In order to find the median of a dataset, we should first order the numbers in the dataset from least to greatest:

29, 22, 23, 31, 29, 29, 22, 23

The smallest number is 22, then 23, then 29, then 31:

22, 22, 23, 23, 29, 29, 29, 31

How many numbers are in this set? 8. An even number!

So we find the mean of the 2 numbers in the middle (23 & 29)

We add these numbers and then divide by 2 (because we have 2 numbers)

[tex]\bf{\displaystyle\frac{23+29}{2}}[/tex]

[tex]\bf{\displaystyle\frac{52}{2}}[/tex]

Which is equal to

[tex]\boxed{\bigstar{\text{Answer:{\boxed{\boxed{26}}}}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

Help picture below problem 14

Answers

Answer:

100

Step-by-step explanation:

Since l and r Parrell lines that means the measure of 4 is 80 since there vertical angles. And then  1 and 4 needs to be supplementary which means the two angles combined equals 180. so 180-80=100

so 1s angle measure is 100

The mean weight of three people in a lift was 62kg. If two of them weighed 55kg each, how much did the third person weigh?

Answers

Answer:

72 kg

Step-by-step explanation:

let weight of third person=x

62-55=x-62

7=x-65

x=7+65=72 kg

A shelf at a grocery store contains 500 packages of corn and flour tortillas. If 22% of the packages are flour tortillas, how many of the packages are corn tortillas?

Answers

Answer:390

Step-by-step explanation:

500*.22=110

500-110=390

390

Answer:

390

Step-by-step explanation:

22% of 500 is 110 so that would make the answer 390 i think

The graph of f(x) is shown. For what values of X does f(x)= 0

-1,1,2
-2,-1,1
-3,-1,1
-1,1,3

Answers

Answer:

-3, -1, 1

Step-by-step explanation:

The values of x when f(x) = 0 are the points on the graph when the curve intercepts the x-axis.

From inspection of the graph, the curve intercepts the x-axis at

x = -3,  x = -1  and  x = 1

Complete the table percent fraction and decimal

Answers

Answer:

140% - 7/5 - 1.4

4% - 1/25 - 0.04

56% - 2.8/5 - 0.56

95% - 19/20 - 0.95

Which rectangular equation represents the parametric equations x = t Superscript one-half and y = 2t? y = 4x2 y = 2x2 y = StartRoot 2 x EndRoot y = 2 StartRoot x EndRoot

Answers

The rectangular equation which represents the parametric equations x =t^(1/2) and y = 2t is; y=2x².

Generating equations from Parametric equations

According to the task content;

It follows that the parametric equations given are; x =t^(1/2) and y = 2t.

Since x =t^(1/2), then it follows that; x² = t.

Therefore, by substituting for t in y= 2t, then we have; y = 2x².

Read more on Parametric equations;

https://brainly.com/question/8674159

Answer:

B on edg!

Step-by-step explanation:

just did the assingment

On average five birds hit the Washington Monument and are killed each week. Joe, an
official, has requested that Congress allocate funds for equipment to scare birds away
from the monument. A congressional subcommittee has replied that funds cannot be
allocated unless the probability of more than three birds being killed in any week
exceeds 70%. Will funds be allocated?

Answers

Answer:

Yes

Step-by-step explanation:

An average of five birds hit the monument each week and in order to receive the funds, more than three birds have to be killed in a week

Determine which of the triangles below are unique. Share your reasoning.
Triangle A: All angle measure 60 degrees
Triangle B: All sides have length 6 cm.
Triangle C: Two sides have length 6 cm, and the included angle measures 55
degrees
Triangle D: Base has length of 6 cm, and the base angles are 50 degrees.

Answers

Answer:

Triangle A and Triangle B

Step-by-step explanation:

I think this is the answer because Triangle A, has a unique that all sides have a measure of 60 degrees. And I also think that Triangle B is unique because It's an Equilateral triangle, which means that all sides have the same length.

So hence, I think the answer is A and B

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

Always keep more than 2 smiles! You have to share them with people who don't have one too, right??

Thanks!

:D

Find the area of the shaded polygons.

Answers

Answer: 372 sq. un

Step-by-step explanation:

7+24=31

Divided by 2 = 15.5

15.5x24 = 372

For a moving object, the force acting on the object varles directly with the object's acceleration. When a force of 45 N acts on a certain object, the acceleration
of the object is 5 m/s?. If the force is changed to 63 N, what will be the acceleration of the object?

Answers

Answer:

acceleration,A = 7

Step-by-step explanation:

F = kA

First expression: 45 = 5k, k = 9

therefore, when F = 63, A = 63/9 = 7

700 mL of Tata cooking oil costs $189. Xtra cooking oil sells for $300 per litre. Which is the better buy? ​

Answers

Answer:

Tata oil

Step-by-step explanation:

0.7 L of Tata cooking oil = $1891 L of Xtra cooking oil = $300

Per 0.1 L

Tata oil = 189/7 = $27Xtra oil = 300/10 = $30

Tata oil is the better buy

Maria is making custom designs using these small trapezoidal prisms. She wants to cover each of the 9 prisms in her current design in floral cloth on all sides. She has 3000 square centimeters of floral cloth.
Does Maria have enough cloth to cover all 9 prisms in her current design?

Choose from the drop-down menus to correctly complete the statement.

The combined surface area of the prisms is
Choose...
cm², therefore Maria
Choose...
have enough cloth for her current design.

Answers

Combined surface area of the 9 prisms is: 3,420 cm².

Maria DOES NOT have enough cloth for her current design.

What is the Surface Area of Trapezoidal Prism?

The surface area of trapezoidal prism = PH + (b1+b2)h

The custom design is a trapezoidal prism.

Find the surface area of one trapezoidal prism given the following dimensions:

Perimeter of trapezoid = P = 5 + 15 + 10 + 10 = 40 cm

b1 = 5 cm b2 = 15 cm h = 7 cm H = 6 cm

Plug in the values into the formula

Surface area of 1 trapezoidal prism = (40)(6) + (5 + 15)7 = 380 cm²

Combined surface area of the 9 prisms = 9 × 380 = 3,420 cm².

Since Maria's flora cloth is 3,000 cm², therefore, she DOES NOT have enough cloth for her current design.

Learn more about surface area of trapezoidal prism on:

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For those of you too lazy to read, here is the answer. :-)

The combined surface area of the prisms is 3420 cm², therefore Maria does not have enough cloth for her current design.

What is the five-number summary of this data set?

{425, 255, 267, 507, 307, 435, 253, 250, 433}
What is the five-number summary of this data set?

{425, 255, 267, 507, 307, 435, 253, 250, 433}

Drag the numbers into the boxes to correctly complete the five-number summary.

Answers

Answer:

min250 max507 Q1=307  Q2=255  Q3=435

Step-by-step explanation:

The five-number summary of this data set is {250, 255, 307, 435, 507}

How to find the mean of a data set?

Mean is the ratio of the sum of the values of the data set to the total number of values available in the data set.

Thus, we get;

[tex]\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}[/tex]

We are given that;

The data set= {425, 255, 267, 507, 307, 435, 253, 250, 433}

Now,

The five-number summary of a data set consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum12.

To find the five-number summary of this data set, follow these steps:

Put the numbers in ascending order: {250, 253, 255, 267, 307, 425, 433, 435, 507}

Find the minimum: The smallest number is 250

Find the maximum: The largest number is 507

Find the median: The middle number is 307

Find Q1: The median of the lower half of the data is 255

Find Q3: The median of the upper half of the data is 435

Therefore, by the mean the answer will be {250, 255, 307, 435, 507}

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A dinner plate has a circumference of 113.04 cm. What is the area of the dinner plate? (Use 3.14 for .)
A.
226.08 cm2
B.
2,034.72 cm2
C.
1,017.36 cm2
D.
56.52 cm2

Answers

option C

hope it helps...!!!

Answer:

[tex]\fbox{Area = 1017.36 sq.cm.}[/tex]

Step-by-step explanation:

Given:

circumference of circular dinner plate= 113.04 cm

To find:

Area of dinner plate = ?

Solution:

circumference = 113.04 cm.

we know that circumference = 2πr

[tex]2 \pi r = 113.04 \: cm \\ r = \frac{113.04 }{2 \pi} \\ r = \frac{113.04 }{2 \times 3.14} \\r = \frac{113.04 }{6.28} \\ \fbox{r = 18 \: cm}[/tex]

We know that,

Area of circle = πr²

now substituting value of r in above formula,

[tex] \pi {r}^{2} = 3.14 \times 18 \times 18 = 1017.36 \: {cm}^{2} [/tex]

[tex] \fbox{Area = 1017.36 sq.cm.}[/tex]

Thanks for joining brainly community!

Which number is a common multiple of 2 and 4?

A) 14

B) 24

C) 26

D) 34

LAST QUESTION MORE POINTS!

Answers

Answer:

Step-by-step explanation:

c I think I did the math that’s what it leads to so yeah

A large grocery store chain pays all workers time and a half on Saturdays and double time on Sundays. If an employee's regular pay is $10.75 per hour, use the expression 10.75(1.5)(x) + 10.75(2)(y) to find their gross income if they worked 4.5 hours on Saturday and 5 hours on Sunday. (4 points)
A.. $156.72
B. $177.38
C. $180.06
D. $257.44

Answers

The gross income earned by the workers if paid time and a half on Saturdays and double time on Sundays is $180.06

How to find gross income

Total = 10.75(1.5)(x) + 10.75(2)(y)

where,

x = hours worked on Saturday = 4.5 hoursy = hours worked on Sunday = 5 hours

Total = 10.75(1.5)(4.5) + 10.75(2)(5)

= 72.5625 + 107.5

= $180.0625

Approximately,

$180.06

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Let f(x)=3/4x2-1 The function g(x) is a vertical stretch of f(x) by a factor of 8.What is the equation of g(x)?

Answers

Answer:

g(x) = 6x^2-1

Step-by-step explanation:

f(x)=3/4x^2 −1.

A vertical stretch by a factor of 8 you multiply the number with x by the factor:

3/4 x 8 = 6

g(x) = 6x^2-1

Solve the equation X=

Answers

Step-by-step explanation:

I think the answer is x=70

A High School’s football Stadium holds a total of 7,000 fans. A survey shows that of the total number of fans, 68% root for the home team. How many fans attending a football game are rooting for the home team? Please help!

Answers

The answer would be 4,760 fans.
Explanation: 7,000 x .68 =4,760
Hope this helps and please mark brainliest!!!

damita uses the pythagorean theorem to write the equation 2k² = j² to represent the triangle shown. Is she correct? Explain.​

Answers

Answer:

Yes, She is correct.

Step-by-step explanation:

Pythagorean theorem:

base² + altitude² = hypotenuse²

k² + k² = j²

Add the like terms. Like terms have same variable with same power.

2k² = j²

Roberto's science grade is calculated using a weighted average. Quizzes are worth 25%, homework is worth 10%, unit tests are worth 30%, and labs are worth 35%.

Roberto earned an average of 94% on his quizzes, 99% on his homework, 92% on his unit tests, and 94% on his labs.

What is Roberto's final science grade?

93.3%

93.9%

94.8%

95.3%

Answers

Answer:

Final grade:  93.9%

Step-by-step explanation:

The weights are as follows:  0.25, 0.10, 0.30 and 0.35.  Note that these add up to the whole, that is, to 1.00.

Then the final grade is:

0.25(94) + 0.10(99) + 0.30(92) + 0.35(94) = 93.9

As Juan continued his hitting practice showing off his abilities, one of the balls flew over the center field stands and into the parking lot. “Did you see that shot”, he yelled at the girls. “The ball hung in the air for at least 10 seconds”, he exclaimed.

The formula for this hit is:
h(x−) = 16+x2 8+3x 4 where h is the height of the ball and x is the number of seconds the ball is in the air.

I need help with part B

Answers

Answer:

  A. Find h(10) = 0 . . . (it is not)

  B. h(5.235) = 0; hang time was about 5.235 seconds

Step-by-step explanation:

The hang time of the ball is the value of x in h(x) such that h(x) = 0.

__

A.

Juan can show the hang time is 10 seconds by finding h(10) = 0. The value of h(10) is ...

  h(10) = -16(10²) +83(10) +4 = -1600 +834 = -766 ≠ 0

Juan cannot prove the hang time was 10 seconds.

__

B.

The hang time is the solution to ...

  h(x) = 0

  -16x² +83x +4 = 0 . . . . . use the given expression for h(x)

  x² -5.1875x = 0.25 . . . . divide by -16

  x² -5.1875x +6.7275390625 = 6.9775390625 . . . . add (5.1875/2)²

  (x -2.59375)² = 6.9775390625 . . . . . . . . . . rewrite as a square

  x = 2.59375 ±√6.9775390625 ≈ {-0.048, 5.235} . . . . square root, find x

The hang time of the ball was about 5.235 seconds.

__

We like a graphing calculator for finding a quick solution to questions like this.

A straight line has gradient - 1/2 and y-intercept 3.
Write the equation of the line in the form of ax + by + c

Answers

Answer:

[tex] - \frac{1}{2} x - y + 3 = 0[/tex]

Step-by-step explanation:

as shown in drawing

what is the awnser to 5+(5x20)x 30

Answers

Answer: 3005

Step-by-step explanation: multiply 5 by 20 and it will give 100 then times 30 Equals 3000 and plus gives 3005 . Please mark brainliest

Answer:3005

Step-by-step explanation :multiply 5 by 20 and it will give 100 then multiply by 30  that Equals 3000 and plus 5 that gives you 3005

A barn is shaped like a rectangular prism with a triangular prism on top as shown. The exterior four walls and two triangular faces need to be repainted. If one gallon of paint covers 232 square feet, how many gallons will it take to repaint the barn? Enter your answer in the box.

Answers

Answer:

23 gallons

Step-by-step explanation:

Given:

A barn is shaped like a rectangular prism with a triangular prism on top as shown.

The exterior four walls and two triangular faces need to be repainted.

To Find:

If one gallon of paint covers 232 square feet, how many gallons will it take to repaint the barn?

Solve:

[tex]12\cdot38\div2\cdot2+84\cdot20+38\cdot20\cdot2[/tex]

= [tex]5336\;square\;feet[/tex]

[tex]\frac{5336}{232}=23[/tex]

Hence 23 gallons to repaint the barn

~lenvy~

I’m not sure the steps to figure out the problem. X = 2 to x =4

Answers

Answer:

you have to put the Y in the formula or make a comparison

A cylinder has a diameter of 10 inches and a height of 14 inches. what is the volume of the cylinder? use 3.14 for pi?
_______cubic inches

Answers

Answer:

Volume of cylinder is 1099 in³

[tex]\\[/tex]

Step-by-step explanation:

[tex]\\[/tex]

Diameter of cylinder = 10 inchesHeight of cylinder = 14 inches

[tex]\\[/tex]

We know that,

[tex]\dashrightarrow \sf \: \: Radius = \dfrac{Diameter}{2} \\ \\[/tex]

[tex]\dashrightarrow \sf \: \: Radius = \dfrac{10}{2} \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: { \underline { \boxed{ \pmb{ \sf{ \pink{ Radius = 5 \: inches}}}}}} \\ \\ [/tex]

Using formula:

[tex] \: \: \: \: \: \: {\underline{\boxed{\pmb{\sf{Volume \: of \: cylinder = \pi r^2h}}}}} \: \pink\star \\ \\ [/tex]

Where,

r is radius of the cylinderh is height of the cylinderπ = 3.14

[tex]\\[/tex]

Substituting the required values in the formula:

[tex]\dashrightarrow \sf \: \: Volume = 3.14 × (5)^2 × 14 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: Volume = 3.14 \times 25 \times 14 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: Volume = 78.5 \times 14 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: { \underline{\boxed { \pmb{ \sf{ \pink{Volume = 1099 \: {in}^{3} }}}}}} \\ \\ [/tex]

Hence,

Volume of the cylinder is 1099 in³

The directions are with the pic below. It’s 2 parts of this equation. I’ll send the other part. Couldn’t all fit on the page.

Answers

Answer:

Step-by-step explanation:

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