Consider the function
f(x) = 8x^3 +1.

If f(g(x)) = x and g(f(x)) = x , find g(x) ?

Answers

Answer 1

[tex]g( \: f(x) \: ) = x[/tex]

And

[tex]f( \: g(x) \: ) = x[/tex]_________________________________

So :

[tex]g(x) = {f}^{ - 1}(x) [/tex]

And

[tex]f(x) = {g}^{ - 1}(x) [/tex]

_________________________________

So to find g(x) , we must find the inverse of f(x) .

Let's do it .....

[tex]f(x) = 8 {x}^{3} + 1 [/tex]

[tex]y = 8 {x}^{3} + 1 [/tex]

Subtract the sides of the equation minus 1

[tex]y - 1 = 8 {x}^{3} [/tex]

Divided the sides of the equation by 8

[tex] \frac{y - 1}{8} = {x}^{3} \\ [/tex]

From the sides of the equation, we take the radical with interval 3

[tex] \sqrt[3]{ \frac{y - 1}{8} } = x \\ [/tex]

[tex] \sqrt[3]{ \frac{1}{8}(y - 1) } = x \\ [/tex]

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

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

So ;

[tex] {f}^{ - 1}(x) = \frac{ \sqrt[3]{x - 1} }{2} \\ [/tex]

Now we find g(x) which is :

[tex]g(x) = \frac{ \sqrt[3]{x - 1} }{2} \\ [/tex]

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer 2

If f(g(x)) = x and g(f(x)) = x , than  [tex]\rm g(x) = \sqrt[3]{\dfrac{x-1}{8}}[/tex] and this can be calculated by finding the inverse of the given function f(x).

Given :

[tex]\rm f(x) = 8x^3+1[/tex]f(g(x)) = x and g(f(x)) = x

Given that f(g(x)) = x it means that:

[tex]\rm g(x) = f^{-1}(x)[/tex]

It is also given that g(f(x)) = x that means:

[tex]\rm f(x) = g^{-1}(x)[/tex]

Now, the inverse of f(x) is given by the following calculation:

[tex]\rm f(x) = 8x^3+1[/tex]

Now, replace f(x) with y in the above equation.

[tex]y = 8x^3+1[/tex]

Now, replace y with x and x with y and evaluate 'y'.

[tex]x = 8y^3 +1[/tex]

[tex]\sqrt[3]{\dfrac{x-1}{8}}=y[/tex]

Now, replace y with [tex]\rm f^{-1}(x)[/tex] in the above equation.

[tex]\rm f^{-1}(x) = \sqrt[3]{\dfrac{x-1}{8}}[/tex]

[tex]\rm f^{-1}(x) = \sqrt[3]{\dfrac{x-1}{8}} = g(x)[/tex]

For more information, refer to the link given below:

https://brainly.com/question/13715269


Related Questions

How do you write –51. 6 as a mixed nuber

Answers

Answer:

-51 6/10 or -51 60/100

Step-by-step explanation:

Find the missing number.
3 + 8 + 4 + 9 = (12 + ____) + 9

Answers

Answer:

3!

Step-by-step explanation:

Add 3+8+4+9, you get 24. 12+9=21. 24-21 is 3! So answer is 3!

What is the answer to 5x + 2 = 3x

Answers

Answer:

x = -1

Explanation:

5x + 2 = 3x

5x - 3x = -2

2x = -2

x = [tex]\dfrac{-2}{2}[/tex]

x = -1

Hope this helps! ☺

Answer:

-1

Step-by-step explanation:

5x+2=3x

2=-2x

x=-1

Write a verbal statement that represents the expression 4+k​

Answers

Answer:

it would be 4k

Step-by-step explanation:

just add 4 and the k which gives you 4k

The sum of 4 and k
......

Convert 250 pesos to U. S. dollars. The exchange rate is 9.99 pesos per U. S. dollar.
options
a. $30.02
b. $240.01
c. $259.99
d. $25.03
e. $2497.50
HELP NEEDED RIGHT AWAY PLS DUE NOW!!!!

Answers

Answer:

D

Step-by-step explanation:

250/9.99=25.0250... Round it to 25.03

The required converted value is $25.03, which is 250 pesos to U. S. dollars.

As we all know, unit conversion is the process of multiplying a provided quantity by a conversion factor that combines the two interconnected units.

To convert 250 pesos to U.S. dollars, we divide the amount of pesos by the exchange rate.

Here, the exchange rate is given as 9.99 pesos per U.S. dollar.

It is the process of assigning a quantity from one unit of measurement to another.

250 pesos / 9.99 pesos per U.S. dollar = 25.025 U.S. dollars

Rounding this to two decimal places, the conversion is approximately $25.03.

Therefore, the correct option is (d) $25.03.

Learn more about the conversions here:

brainly.com/question/3810064

#SPJ6

the sum of 1/11 and 5/11

Answers

Answer:

6/11

Step-by-step explanation:

1/11+5/11

Answer:

the sum of 1/11 and 5/11 is 6/11

Step-by-step explanation:

the sum would mean addition so

1/11 + 5/11

when adding fractions you don't add the denominator

so then you'd only add 1 + 5 which gets you 6

so 6/11

10 pls 10 I dnt no wat to do

Answers

10 plus 10 is 20 lol

What value of x satisfies the equation below?
x +x=12
3 6

A. x=12
B. x=6
C. x=24
D. x=72​

Answers

I believe the answer would be B, but I don't understand what the 3 and 6 are for due to there being no context.

Complete the long division problem on your own sheet of paper. Then, fill in the digits.

47 dived by 9598 do the whole problem

Answers

Answer:

204 Remainder 10 / 204 10/47

Step-by-step explanation:

Answer:

  0 2 0 4

4 7 9 5 9 8

 − 0      

   9 5    

 − 9 4    

     1 9  

   −   0  

     1 9 8

   − 1 8 8

       1 0

Step-by-step explanation:

the answer is 10

Which property explains why these two expressions are equal?

a(b + c) = a(c + b)

Answers

Answer:

The Associative Property.

Answer:

They are equal because no matter how you flip an addition equation, the result will always be the same. aka the associative property.

Step-by-step explanation:

Because variable a never moved, but b and c did, the answer remains the same.

example: x + y = y + x

What is the difference between Glasgow and Copenhagen. (Glasgow= -7.8 Copenhagen=-3.8)

Answers

Answer:

Step-by-step explanation:

The difference of the two values is 4 as calculated by subtraction.

An arithmetic operation called subtraction is the process of deleting or removing items from a collection. The negative symbol (-) denotes subtraction.

Subtraction can mean eliminating or lowering physical and abstract quantities utilizing a variety of things, such as fractions, matrices, vectors, irrational numbers,  decimals, functions, and  however negative integers. it is typically linked with natural numbers in mathematics.There are several significant patterns in subtraction. It is anticommutative, which means that altering the sequence alters the answer's sign. Additionally, it is not associative, which means that when subtracting more than two numbers, the method used matters. 0 is the additive identity, hence subtracting it has no effect on a number. In relation to related operations like addition and multiplication, subtraction also abides by predictable principles.

The given values for Glasgow and Copenhagen are given as -7.8 and -3.8 .

Therefore difference = -3.8 - (-7.8) = -3.8 +7.8 = 4

To learn more about subtraction visit:

https://brainly.com/question/2346316

#SPJ1

If three boxes of pasta cost $5.79, find the cost of 22 boxes.

Answers

Answer:

Step-by-step explanation:

3 boxes of pasta --> $5.79

1 box of pasta --> $5.79/3=$1.93

22 boxes of pasta --> $1.93 x 22 =$42.26

The answer would be 42.46

How I got the answer divide 5.79 by 3 three multiply the answer by 22 then you get the answer

What will the 15th term in the sequence be? 2.2, 4.4, 6.6, 8.8,

Answers

Answer:

30.30

Step-by-step explanation:

Just count up by 2 each time.

What is an equivalent ratio to 9/15?

Answers

Answer:

the answer is 3/5

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

I’m just different

Which vehicle has the better gas mileage? Explain your reasoning.

Answers

Answer:

Tesla because it has no gas

How can ΔWXY be mapped to ΔMNQ?

Triangles W X Y and M N Q are shown. The lengths of sides M N and W X are 18 centimeters. The lengths of sides Y W and M Q are 30 centimeters. Angles Y W X and N M Q are congruent. Triangle W X Y is slightly up and to the right of triangle M N Q. Angle Y W X is the bottom angle and angle N M Q is the left angle.

Translate vertex W to vertex M, then reflect across the line containing _______________.

Answers

Answer:

A. WX

Step-by-step explanation:

May I have brainliest please? :)

Triangle WXY can be mapped to triangle MNQ by:

Translating vertex W to vertex M.Then, reflect ΔWXY across the line containing line segment WX.

What is transformation?

Transformation involves changing the size and the position of a shape

From the figure (see attachment), we have the following highlights

Both triangles are not on the same height (i.e. translation is required)Both triangles are not on the same orientation (i.e. one of the triangles need to be reflected)

Hence, Triangle WXY can be mapped to triangle MNQ by translating vertex W to vertex M, and then, reflecting ΔWXY across the line containing line segment WX.

Read more about transformation at:

https://brainly.com/question/4057530

Any help on this maths question will be truly appreciated ​

Answers

Step-by-step explanation:

Hey there!

1. 》 (√5)^2*(√3)^2

Cancel sqrt and square.

[tex]5 \times 3[/tex]

= 15

2.

[tex] = { (\sqrt[ 3]{9} )}^{3} \times ( { \sqrt{30}) }^{2} [/tex]

Cancel sqrt and square and also cubeoot and cube.

[tex]9 \times 30[/tex]

= 270

Hope it helps....

6. Write an equation of a line that passes through the points (4,5) and (8,3).

Answers

Answer:

The answer to your question is -2/4

Step-by-step explanation:

y2-y1

x2-x1

I need help pleasseseeee

Answers

Answer:

D, 110$

Step-by-step explanation:

According to the systematic function, given that the bill as a function is equal to one tenth the quantity of x for kilowatt hours less than or equal to 200, and three twentieths of 200 less than the quantity of x plus 20 for kilowatt hours greater than 200. The answer is 110$ because the question gives us a measure of kilowatts greater than 200 so the second equation is used in the system. Therefore .15(800-200) + 20 = b(800), (.15)600 +20 = 90 + 20 = 110

Solve x-(-9) = -14.
0-5
0 23
0-23
O 5

Answers

Step-by-step explanation:

x - (-9) = -14

x = -14 +(-9)

x = - 23

if you wanna check,

-23 - (-9) = -14

-14 = -14

Me ayudan por favor??
¿Qué tres números consecutivos suman 156?

Answers

Answer:51+52+53Step-by-step explanation:

De tal forma que los números son: 51-52-53. Comprobando estos tres números consecutivos enteros: 51+52+53=156.

espero que esto te ayude :)

Answer 51+52+53


Explanation

What 3 numbers can be multiplied together to get 180?

Answers

2×6×15=180

Step-by-step explanation:

2×6=12

12×15=180

Answer:

3×6×10=180

Step-by-step explanation:

.............. there can be more than one right answer for this

Determine if segments JK and LM are parallel, perpendicular, or neither.

J(-10, -7) K(-4, 1) L(-1, 1) M(-6, -2)

Answers

Answer:

perpendicular

Step-by-step explanation:

the lines meet together

Can you find the mistake?

Answers

Answer:

14b +64

Step-by-step explanation:

as listed above

-4 5/1 as a simplified fraction?

Answers

The answer is 1/1 or 1

During a musical, an orchestra is playing. As the music plays, the volume changes at the beginning of the piece can be modeled by the equation s = 10│x - 4│+ 50 where s represents the sound level in decibels and x represents the number of measures of music played. Explain in words each step to find the following question:



At what number(s) measures played would the sound level be at 80 decibels?

Answers

Answer:

what

Step-by-step explanation:

...

To find the range for the number of measures played to satisfy our solution, we must solve for x using s = 80.
Next, we subtract 50 from both sides of the equation.
Next, we divide both sides of the equation by 10
Next, to eliminate the absolute value bars, we will add a ± sign in front of our s value, 3.
Finally, we add 4 to both sides of our equation giving us 4 ± 3 = x
Separating this into two equations, we get 4 - 3 = x and 4 + 3 = x
Therefore, x, the number of measures of music played, must be either 1 or 7.

Sofia wants to rent an apartment. She visits Apartment A which charges $100 for a one-time deposit and $400 per month for rent. She also visits Apartment B which charges $500 for a deposit, but only charges $350 per month in rent. Write and solve an inequality that shows how many months it would take for the total paid to be less for Apartment B.

Answers

Credit To: "lublana" On Brainly For This Answer

Answer:

Given that one time charge of appartment "a" = $100

Given that monthly rent of appartment "a" = $400

say the number of months = x

then total cost of the rent for apartment "a" = 100+400x

Given that one time charge of appartment "b" = $500

Given that monthly rent of appartment "b" = $350

then total cost of the rent for apartment "b" = 500+350x

Now we have to make an inequality so that number of months it would take for the total paid to be less for apartment b.

that means 100+400x is less than 500+350x

Hence required inequality is 100+400x<500+350x.

Now we have to solve this inequality.

400x-350x<500-100

50x<400

divide both side by 50

x<8

hence final answer is number of months should be less than 8.

A cedar board is 2 inches long and 8 feet long. You will need to cut down the length of the board into 1 1/3 inches long. How many pieces can u cut from an 8 inch long board

Answers

Answer:

You will be able to cut at least 6 pieces

Step-by-step explanation:

At a music store, 8 CDs cost 32$. How much will 15 CDs cost at this store?

Answers

Answer:

$60

Step-by-step explanation:

First we have to find the default cost for a single CD.

8 ÷ 32

Divide.

8 ÷ 32 = 4

Now that we have the default cost, we have to find the price for 15 CDs.

4 x 15

Multiply.

4 x 15 = 60

32/8 = 4, therefore each CD costs $4. 4 x 15 = $60.

Solve for r:
3x + 2 = 11
11
O A
B. 3
Oc.
3
OD.
13
3
O E 6

Answers

Do you mean solve for x? Which is 3

Answer:

B

Step-by-step explanation:

3x + 2 - 2 = 11 -2

3x = 9

3x divided by 3 = 9 divided by 3

x=3

Other Questions
Which of the following is the valid classification of the system given below?$ 7x + 2y = 24| 2x + 1 = y Last week, Ralphs gerbil drank 20 mL of water. This week he drank 16 mL of water. By what percent did the gerbils intake of water decrease? help plz with this i nead it done soon did you parcitipate in any religious activities recently? can someone please help me Completa las frases con la(s) palabra(s) apropiada(s) del vocabulario del captulo, segn los dibujos.Estamos en una sala de clases donde no hay ni un ____ libre. What is in the blank? Evaluate. Write your answer as a fraction or whole number without exponents. Determine the degree of the polynomial -57 Write a recursive rule using the table.(2 Points)n1 2 3 4 5f(n)-3.4 -3.4 -2.1-0.80.51.8 PLEASE HELP WITH THIS HISTORY QUESTION in the game of croquet, a player moves a ball around a course by striking the ball with a mallet all the players take turns striking there own balls the photo shows some kind of result of one kind of play.what most likely causes the motion of the purple ball in the photo. Read the excerpt from Act I of The Importance of BeingFarnest.The epigram that Algernon uses in his last line providesa critique aboutJack. Of course it's mine. [Moving to him.) You haveseen me with it a hundred times, and you have no rightwhatsoever to read what is written inside. It is a veryungentlemanly thing to read a private cigarette case.Algernon. Oh! it is absurd to have a hard and fast ruleabout what one should read and what one shouldn't.More than half of modern culture depends on what oneshouldn't readO how the rules of Victorian society were not very strictand were not taken seriously.O how members of the upper class were not concernedwith the rules of society and rarely followed them.O how the rules of Victorian society dictated manythings, even what was proper to read.Ohow members of high society rarely read books andwere not concerned with cultural knowledge. seven is 10 times the value of which number 0.007 0.7 0.07 70 Find area of triangle. Picture included. lebal this plz i need it Two random variables x and y are independent if the value of x does not affect the value of y. If the variables are not independent, they are dependent. A new random variable can be formed by finding the sum or difference of random variables. If a random variable x has mean x and a random variable y has mean y then the means of the sum and difference of the variables are given by the following equations. x+y=x+y xy=xy The distribution of a test's scores for college-bound male seniors has a mean of 1528 and a standard deviation of 319. The distribution of a test's scores for college-bound female seniors has a mean of 1498 and a standard deviation of 304. One male and one female are randomly selected. Assume their scores are independent.What is the average sum of their scores? What is the average difference of their scores? Radius 2.9cm whats the circumference the perspective from which the story is told is called the (x^2+3x)=(x^2+x+2)is it a or ba. x=2b. x=1 Carpeting cost $7.99 a yard. If Jan buys 12.4 yards, how much will it cost her?