are f(x)=1/8x^3 and g(x)=2x^1/3 inverses of each other? Check all that apply.
PLEASE SHOW WORK!
The simplified expression for f(g(x)) is x.
The simplified expression for f(g(x)) is One-fourth x.
The simplified expression for g(f(x)) is 2x.
The simplified expression for g(f(x)) is x.
The functions are inverses of each other.
The functions are not inverses of each other.

Answers

Answer 1

Answer: 1,4,5

Step-by-step explanation:

Answer 2

The correct options are, The simplified expression for g(f(x)) is x.

The functions are not inverses of each other.

What is an inverse function?

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, f(x) = 1/(8x³).

f(x) = 1/(2x)³.

y = 1/(2x)³.

(2x)³ = 1/y.

[tex]2x = \frac{1}{y^\frac{1}{3}}[/tex].

[tex]x = \frac{1}{2y^\frac{1}{3}}[/tex].

[tex]f^{-1}(x) = \frac{1}{2x^\frac{1}{3}}[/tex] and g(x) = [tex]2x^\frac{1}{3}[/tex] so, they are not inverses of each other.

Now, f(g(x)) = [tex]\frac{1}{8((2x)^\frac{1}{3})^3}[/tex].

f(g(x)) = 1/16x.

g(f(x)) = [tex]2(1/8x^3)^\frac{1}{3}[/tex].

g(f(x)) = x

learn more about the inverse of functions here :

https://brainly.com/question/2541698

#SPJ2


Related Questions

Which coordinate pair identifies a point in the third quadrant of the coordinate plane?

Answers

Answer:

-,-

Step-by-step explanation:

the y axis is negative and the x axis is also negative

hope this helps

1+cosx/1-cosx=tan^2x/(sec^2-1)^2

Answers

Answer:

Take a look at the attachment below

Step-by-step explanation:

A ramp is 35 ft long rises to a platform. The bottom is 15 ft from the foot of the ramp. Find x, the angle of elevation of the ramp. Round your answer to the nearest tenth of a degree.

Answers

Answer:

The angle of elevation of the ramp is 64.60°

Step-by-step explanation:

Given;

length of the ramp, L = 35 ft

distance of the platform to the foot of the ramp, d = 15 ft

The length of the ramp forms the hypotenuse side of this right angled triangle;

The angle of elevation of the ramp is in angle between the hypotenuse and adjacent side of the triangle.

Cos x =  adjacent / hypotenuse

Cos x = 15 / 35

Cos x = 0.4286

x = Cos⁻¹ (0.4286)

x = 64.62

x = 64.60°

Therefore, the angle of elevation of the ramp is 64.60°

In what ways are driverless cars safer than human drivers?

Answers

Answer:

Driverless cars may be safer than cars with drivers because they do not get tired or distracted, and they do not engage in risky driving practices such as speeding and/or texting while driving, drinking and driving, etc..

Step-by-step explanation:

Edg. 2020

Answer:Driverless cars may be safer than cars with drivers because they do not get tired or distracted, and they do not engage in risky driving practices such as speeding and/or texting while driving, drinking and driving, etc..

Step-by-step explanation:


help please! which point on the number line below bests represents this?

Answers

Answer:

Point M

Step-by-step explanation:

3x+⅝>4x-½ select from the drop down menus to correctly justify each step.​

Answers

Step-by-step explanation:

3x-4x>-1/2-5/8

-x>-9/8

x<9/8

For each pair of polygons, describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.

Answers

Answer:

1. It is a reflection across the y axis, a rotation and a translation to the right and down.

2. A reflection across the x-axis, translation left 2 and down 1, with a 45 degree clockwise rotation.

3. An 180 degree reflection on line bc and a translation

Step-by-step explanation:

Case 1 involves translation and rotation.

Case 2 involves translation, rotation and reflection.

Case 3 involves translation and reflection.

In this question, we are going to describe succinctly all Steps needed to turn each Polygon P into respective Polygon Q:

Case 1:

(i) Translation along a Vector between Points A and H.

(ii) Rotation around Point H.

Case 2:

(i) Translation along a Vector between Points B and J.

(ii) Rotation around Point J.

(iii) Reflection with respect to a "vertical" Lines passing through Point J.

Case 3:

(i) Translation along a Vector between Points B and F.

(ii) Reflection with respect to a Line passing through Segment FD.

Please see this question related to Operations with Polygons: https://brainly.com/question/12091224

Solve for p in the Ilteral equation 3p + 4r = q.

solve for p

Answers

Answer:

p = [tex]\frac{q}{3} - \frac{4r}{3}[/tex]

Step-by-step explanation:

Convert 15°C to °F (to the nearest tenth).

Answers

The answer is 60 Fahrenheit

15°c = 59°f

because :

(15 °C × 9/5) + 32 = 59 °F

===

so to the nearest tenth its doing 60°f

[Giving Brainleist] What is 4x+2?

Answers

Answer:

4x + 2 = 0

4x = -2

x = -1/2

if you need it simplified it already is

Simplify the expression
3-5(2x-5)

Answers

Answer:

-10x + 28

Step-by-step explanation:

Step 1: Write expression

3 - 5(2x - 5)

Step 2: Distribute -5

3 - 10x + 25

Step 3: Combine like terms

-10x + 28

Answer:

= -10x+28

Step-by-step explanation:

subtract -9x-7 from 8x2 -5x +9​

Answers

Answer:

8x2+4x+16

Step-by-step explanation:

first you would place as so

8x2-5x+9 - (-9x-7)

you would then change question to addition but do this you would have to switch the signs for the one in the parenthisis. it would look like 8x2-5x+9 + 9x+7

You then add like terms and put them into standard form.

hope this helps!!

Dao receives an employee discount on the purchase of a new automobile. The automobile that he is interested in has a sticker price of $18,560. If his discount is 18 percent, what is the price that Dao will pay?
$3,340.80
$3,712.00
$12,992.00
$15,219.20

Answers

Answer:

D. $15,219.20

Step-by-step explanation:

given:

The automobile that he is interested in has a sticker price of $18,560.

If his discount is 18 percent,

find:

what is the price that Dao will pay?

solution:

sale price =   $18,560 - (0.18 x  $18,560) =  $15,219.20

therefore,

Dao will pay $15,219.20

the answer is D.

im taking the test right now..

Which has the lowest unit price ?

Answers

Answer:dd

Step-by-step explanation:d

Answer:

The answer is $0.33 for 11 oz

Step-by-step explanation:

All you have to do is divide the oz by the price and A is the lowest.

I NEED HELP PLEASE PLEASE HELP ME :(

Answers

Answer:

-1/125

Step-by-step explanation:

1/(-5)^3

evaluate

1/-125

Solve for j. please help meee

Answers

Answer:

112 degrees

Step-by-step explanation:

Angle J and the other angle combines to form a straight angle. In other words, they must total 180 degrees. Thus:

[tex]68+j=180[/tex]

Subtract 68 from both sides:

[tex]j=112\textdegree[/tex]

And we're done!

Answer:

I believe the answer is 112 degrees

Step-by-step explanation:

If you know, a straight line hs 180 degrees. Well, then having this knowledge,  make a simple equation x+68=180.

Then Solve the equation

x+68=180

  -68  -68

x=112

Hope it helps!

Please help me solve this question with full solutions!!!

Answers

Answer:

first

|a+3|/2=1

|a+3|=1*2

|a+3|=2

a=2-3

so,a=-1

second

2|b+1|=6

|b+1|=6/2

|b+1|=3

b=3-1

so,b=2

now,|a+b|

= -1+2

= 1

therefore,|a+b|= 1

Order of Operations

If the Order of Operations did not exist, how many

possible solutions can you find for this expression?

4 + 9 + 16 : 4 - 8 – 3 x 5

Answers

Given:

[tex]4 + 9 + 16 \div 4 - 8 -3 \times 5[/tex]

To find:

The number of possible solutions, if the Order of Operations did not exist.

Solution:

We have,

[tex]4 + 9 + 16 \div 4 - 8 -3 \times  5[/tex]

Now,

Case 1:

[tex][4 + 9 + 16] \div [4 - 8 -(3 \times  5)]=29\div (4 - 8 -15)[/tex]

[tex]4 + 9 + 16 \div  4 - 8 -(3 \times  5)=-\dfrac{29}{19}[/tex]

Case 2:

[tex][4 + 9 + 16] \div  (4 - 8 -3) \times  5=29\div  (-7\times 5)[/tex]

[tex]4 + 9 + 16 \div  (4 - 8 -3) \times  5=-\dfrac{29}{35}[/tex]

Case 3:

[tex]4 + 9 + (16 \div 4) - 8 -(3 \times  5)=4+9+4-8-15[/tex]

[tex]4 + 9 + (16 \div 4) - 8 -(3 \times  5)=-6[/tex]

Many more possibilities are there.

Therefore, there are more than 3 possible solutions.

A sporting goods sold 2.5 times as many football as basketball last year drag footballs to represent the number of football sold for every 2 basketball sold.

Answers

Answer:

5 footballs were sold for every 2 basketballs sold.

Step-by-step explanation:

2.5 times as many football as basketball was sold last year

This can be represented as

1 basket ball sold = 2.5 footballs sold

for every 2 basketball sold, number of football sold = 2.5 x 2 = 5 footballs

I NEED HELP EXPLAINING HOW I GOT MY ANSWERS ILL GIVE AS MANY POINTS POSSIBLE

Answers

Answer:

Step-by-step explanation:

solve for h in h+6/5=2

Answers

Answer:

h=4/5

Step-by-step explanation:

[tex]h + \frac{6}{5} = 2 [/tex]

Collect like terms and simplify

[tex]h = 2 - \frac{6}{5} \\ h = \frac{4}{5} [/tex]


What is the value of m in the equation {m- n = 16, when n = 8?




Answers

Answer:

m=44

Step-by-step explanation:

Answer:

m=44

Step-by-step explanation:

>

Please help!!! Do In 20 minutes

Answers

Answer:

The side length of the square would be (b - a) , so I believe the answer would be the one you have highlighted.

Please help! (-5)(16)(-3)(-2)

Answers

Answer:

-480

Step-by-step explanation:

(-5)(16)(-3)(-2) =

= (-80)(-3)(-2)

= (240)(-2)

= -480

The temperature was -1 °F, 5 °F, 8 °F, and 6 °F. What was the average temperature?

Answers

4.5 °F is the average temperature

Answer:

4.5

Explanation:

add up all the numbers and divide by the amount

(GIVING BRISTLIEST) What is 50x+100x-50y?

Answers

Answer:

[tex]50(3x-y)[/tex]

Step-by-step explanation:

You just gave an expression, therefore:

[tex]50x+100x-50y[/tex]

[tex]150x-50y[/tex]

[tex]50(3x-y)[/tex]

[tex]\framebox{\parbox[t][1.0cm]{4.50cm}{\addvspace{0.2cm} \centering $ \;\; \, \;\; \;\; 150x+-50y $ } }\\[/tex]

Step-by-step explanation:

Let's simplify.

[tex]50x+100x-50y[/tex]

To solve this, we will have to combine the like terms.

[tex]50x+100x+-50y[/tex]

Let's add parenthesis.

[tex](50x+100x)+(-50y)[/tex]

This equals:

[tex]150x+-50y[/tex]

Hope this helps!

Point T is on line segment \overline{SU} SU . Given TU=4x+1,TU=4x+1, SU=8,SU=8, and ST=3x,ST=3x, determine the numerical length of \overline{TU}. TU .

Answers

Answer:

5

Step-by-step explanation:

If point T is on the line SU, then ST+TU = SU. Given  TU=4x+1, SU=8, and ST=3x

Substituting the given values into the expression ST+TU = SU

8 = 3x+4x+1

8 = 7x+1

collect like terms;

7x = 8-1

7x = 7

Divide through by 7

7x/7 = 7/7

x = 1

Substitute x = 1 into the expression TU = 4x+1 to get the length of TU

TU = 4(1)+1

TU = 4+1

TU = 5

Hence the length of TU is 5

Answer:

Step-by-step explanation: the answer is 5

James earns $8.75 per hour working at the Kroger after school. He needs at least $250 for an iPhone. Write and solve an inequality that describes how many hours James must work to buy the iPhone.

Answers

Answer:

29 hours

Step-by-step explanation:

$250: $8.75= 28.5. and you round that up to 29. cause 28 times 8.75 is $245. and that's below the amount that James needs

Pls help im timedTrey converted 12,500,000 into scientific notation as 12.5 * 10 to the power of 6 his he correct

Answers

Answer:

12,500,000 (twelve million five hundred thousand) is an even eight-digits composite number following 12499999 and preceding 12500001. In scientific notation, it is written as 1.25 × 107.

Step-by-step explanation:

The temperature at noon at a ski resort is 3 degrees F. The temperature drops 8 degrees F by midnight. What is the temperature at midnight?

Answers

Answer:

-5 degrees F

Step-by-step explanation:

Well if the original tempeture was 3 and it drops by 8 you would add 3+8 which is 11
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