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 (2025)

Mathematics High School

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

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Related Questions

Which of the following expresses the sum of 54 and 30 as a product? * O 6 (54 + 30) O 6(9+5) O 9 (6+5) O 9 (54 + 30)​

Answers

6(9+5)

Step-by-step explanation:

Which of the following fractions is an improper fraction?
2/3
6/11
21/25
8/7

Answers

Answer:

8/7

Step-by-step explanation:

The Numerator is bigger than the denominator which in turn can be converted to a mixed fraction.

I have a math question g=mB-2qB and I have to solve for B​

Answers

Answer:

[tex]B = \frac{g}{m-2g}[/tex]

Step-by-step explanation:

Given

[tex]g = mB - 2qB[/tex]

Required

Solve for B

[tex]g = mB - 2qB[/tex]

Factorize the expression

[tex]g = B(m - 2q)[/tex]

Divide both sides by m - 2g

[tex]\frac{g}{m-2g} = \frac{B(m - 2q)}{m-2g}[/tex]

[tex]\frac{g}{m-2g} = B[/tex]

Reorder

[tex]B = \frac{g}{m-2g}[/tex]

i need help because i do need help

Answers

Answer:

Step-by-step explanation:

the perimeter to ABCD is 13

the perimeter to WXYZ is 32.5

the scale factor enlargement is 2.5

A football team lost 5 yards on each of 3 plays.Explain how you could use a number line to find the teams change in field position after 3 plays.Then find and interpret the change in position

Answers

Answer:

Kindly check explanation and attached picture

Step-by-step explanation:

Given that:

A football team lost 5 yards on each of 3 plays

Using a number line we could show the loss in yard after each play. With a loss of 5 yards after each play, there will be a total of:

(Number of plays * yards lost) = (3 * 5) = 15 yards

The attached picture shows a number line moving a distance of 5 yards to the left ( negative direction) after each play after which it arrives at a total loss of 15 yards after the third play.

Joseph grew 2 centimeters in 12 weeks how much is this in inches per year

Answers

Answer:

About 3.41 inches per year

Step-by-step explanation:

2 cm per 12 week

52 weeks in a year

52/12 = about 4.33

2 cm * 4.33 = about 8.67 cm

2.54 cm = 1 inch

8.67/2.54 = about 3.41 inches per year

Hope this helps!

(pls mark brainliest)

-8(x - 7)

(Distributive property)

Answers

Answer:

-8x+56

Step-by-step explanation:

we have to multiply 8 by x and -7

-8 times x is -8x. However -8 times -7 is POSTIVE 56

Answer:

So the answer to this problem would be -8x+56

Step-by-step explanation:

The reason for this is -8 multiply by x and multiply by -7 so if you multiply -7 and -8 together u will get 56 and -8 multiplied with x is = -8x

Hope that helps

Which graph is generated by this table of values? x –5 –3 –1 4 y 2 4 1 0 On a coordinate plane, points are at (negative 5, 2), (negative 3, 4), (negative 1, 1), and (4, 0). On a coordinate plane, points are at (negative 5, negative 2), (negative 3, negative 4), (negative 1, negative 1), and (4, 0). On a coordinate plane, points are at (0, 4), (1, negative 1), (2, negative 5), and (4, negative 3). On a coordinate plane, points are at (1, negative 1), (3, negative 4), (4, 0), and (5, negative 2).

Answers

Answer:

The answer is A

Step-by-step explanation:

All you must do is find the correct values in the graph.

The graph which is generated by the table of values x -5,-3,-1,4 and y=2,4,1,0 is on coordinate plane points are at (-5,2) ,(-3,4) ,(-1,1) ,(4,0).

What is function?

A function is a relationship between two or more variables having each value of x corresponding to y values. Values of x are known as domain and values of y are known as codomain.

How to graph function?

We have been given the following table as under:

x y

-5 -3

-3 4

-1 1

4 0

We have to plot the points -5 ,-3,-1,4 on x axis and corresponding-3,4,1,0 on y-axis.

Hence the graph of given table of values is that on coordinate plane points are at (-5,2) (-3,4)(-1,1)(4,0).

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Find the distance of each segment AB and CD. You may leave in radical form. A (3, 4) B(1, 0) and C (-1, 2) D (-2, 5)

Answers

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

AB

[tex]\sqrt{(1-3)^2+(0-4)^2}[/tex]

[tex]\sqrt{4+16}[/tex]

[tex]\sqrt{20}[/tex]

[tex]2\sqrt5[/tex]

CD

[tex]\sqrt{(-2-(-1))^2+(5-2)^2}[/tex]

[tex]\sqrt{1+9[/tex]

[tex]\sqrt{10}[/tex]

Hope this helps.

頑張って!

Answer:

Step-by-step explanation:

se the graph to determine the input values that

correspond with f(x) = 1.

O x=4

O x= 1 and x = 4

O x= -7 and x = 4

O x= -7 and x = 2

6.

(-6, 4)

4

(1,4)w

2

(-7, 1)

(2, 1) xw

2

4

-8/ -6 -4 -2e

-2

-4thrrt

BIG IDEAS MATH

Chapter2-Section2
i
Write a function g whose graph represents a reflection in the y-axis of the graph of f(x) = -x+1.
g(x) =
Help!!!

Answers

Answer:

f(x) = -x+1

to find x-intercept/zero substitute f(x)=0.

0=-x+1

0=-x+1 move variable to the left-hand side and change its sign.

x=1

PLEASE HELP! this is due today!

Answers

Answer:

For question 9 = 54

Step-by-step explanation:

54 + 67 = 121

67 - 54 = 13

Answer:1.)k+2x 2.)54 3.) i think is n+n=145

Step-by-step explanation:

Simplify.
7/11 -3/11

Answers

Answer:

4/11

Step-by-step explanation:

7/11-3/11

=>(7-3)/11

=>4/11

Sam takes the bus 3/5 of the distance from home to school. He then walks one block to his friends house and rides with the friend the remaining seven blocks to school. What fractional part of the trip did he ride with his friend?

Answers

Answer:

2/5

Step-by-step explanation:

3/5 + ____ = 5/5

2/5

Can someone plss help mee ??

Answers

first - 8
second - 4
third - 12
fourth - 9

what is x + -14 = -3 -15, i am really struggling with math at the moment

Answers

Answer:

X=_42

Step-by-step explanation:

X+(_14)=_3_15

X+(_14)=_3_15 X=_14=_18

X+(_14)=_3_15 X=_14=_18X=_18_14

X+(_14)=_3_15 X=_14=_18X=_18_14X=_42

which of the following expressions is equal to -20​

Answers

Answer:

no expression is equal to -20

find the distance between each points (-1,4) (1,-1)

Answers

Answer: The distance is about 5.39 units

Step-by-step explanation:

To find the distance between the two points find the difference in the x and y coordinates and square them to add them and find their square root.

4-(-1) = 5

-1 -1 = -2

5^2 + -2^2 = d^2 where d is the distance

25 + 4 = d^2

29 = d^2

d = [tex]\sqrt{29}[/tex]

d= 5.39

Determine the intercepts of the line. −5x+9y=−18

Answers

Answer:

try using desmos its a graphing calculator

Step-by-step explanation:

Answer:

x intercept = (3.6, 0)

y intercept = (0, -2)

Step-by-step explanation:

i did this on khan academy so it's easy

you're welcome

The endpoints of AB are A(2,5) and B(4,3). What are the coordinates of the midpoint of
AB?

Answers

Answer:

(3,4)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(2+4)/2 = 6/2 =3

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(5+3/2 = 8/2 =4

The midpoint is (3,4)

Answer:

Hey there!

Using the midpoint formula we find the midpoint to be: (3, 4)

Let me know if this helps :)

is √324 rational, irrational, an integer, or a natural or whole number

Answers

Answer:

wHOLE number

Step-by-step explanation:

IT is a whole number

What is the product? (3x-6) (2x2-7x+1)

Answers

The product is 6x^3-33x^2+45x-6

HELPP
Solve the equation 15+25=4+6x

Answers

Answer:

x=6

Step-by-step explanation:

Answer: x=6

Explanation:

1. Add: 15+25=40

2.Subtract 4 from each side: 40=4+6x

3.Divide by 6: 36=6x

4. x=6

The diagonal of a square is 10m long. What is the length of the side of the square?(Give your answer to the nearest cm)

Answers

Answer: 500 sqrt(2)cm

Explanation:

Form: d = a sqrt(2)

Where d = diagonal = 10m and a = side length

10 = a sqrt(2)
10/sqrt(2) = a

Rationalize the denominator:
10/sqrt(2) x sqrt(2)/sqrt(2)
= 10 sqrt(2)/2
= 5 sqrt(2)

Thus, a = 5 sqrt(2)m

Change to cm:
5 sqrt(2) x 100cm = 500 sqrt(2)cm

What is the simplified expression for 5 to the power of 4 multiplied by 5 to the power of 3 over 5 to the power of 5

Answers

Answer:

25

Step-by-step explanation:

5^4 x 5^3/5^5

5^(3+4)/5^5

5^7/5^5

5^(7-5)

5^2

25

Answer:

5 to the power of 2.

Step-by-step explanation:

Simplify 12 to the 3rd over 12 to the 7th

Answers

Answer:

0.0000482253

Step-by-step explanation:

A sports stadium has 10000 seats, divided into box seats, lower-deck seats, and upper-devk seats. Box seats sell for 10 dollars, lower-deck seats sell for 8 dollars, and upper-deck seats sell for 5 dollars.If all the seats are sold, the total revenue for a game is 70000 dollars.The stadium has 4 times as many upper* deckseats as box seats.How many lower-deck seats are in the stadium?

Answers

Answer:

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000

Step-by-step explanation:

Let number of box seats = [tex]x[/tex]

Let number of lower deck seats = [tex]y[/tex]

Let number of upper deck seats = [tex]z[/tex]

As per question statement:

[tex]x+y+z=10000[/tex] ...... (1)

Cost for box seat = $10

Cost for [tex]x[/tex] box seats = 10[tex]x[/tex]

Cost for lower deck seat = $8

Cost for [tex]y[/tex] lower deck seats = 8[tex]y[/tex]

Cost for lower deck seat = $5

Cost for [tex]z[/tex] lower deck seats = 5[tex]z[/tex]

As per question statement:

[tex]10x+8y+5z=70000[/tex] ..... (2)

[tex]z = 4x[/tex] ..... (3)

Putting value of [tex]y[/tex] in (1) and (2):

[tex]x+y+4x=10000\\\Rightarrow 5x+y=10000[/tex] ....... (4)

[tex]10x+8 y+5\times 4x=70000\\\Rightarrow 30x+8y=70000 ..... (5)[/tex]

8 [tex]\times[/tex] (4) - (5):

[tex]10x =[/tex]10000

[tex]\Rightarrow x = 1000[/tex]

By (3):

[tex]z = 4000[/tex]

Now, by equation (1):

[tex]y[/tex] = 5000

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000

2/5 as a decimal show all work

Answers

Answer:

0.4

Step-by-step explanation:

to convert from a fraction to a decimal, we first have to make the denominator 100

we know that 5 goes into 100 20 times ;

100 ÷ 5 = 20 ;

then we have to multiply the numerator by 20 as well because we have multiplied the bottom by 20 ;

[tex]\frac{2}{5}[/tex] [tex](\frac{20}{20})[/tex]

2 x 20 = 40 ;

= [tex]\frac{40}{100}[/tex]

then to convert this into a decimal, divide the numerator by the denominator

40 ÷ 100 = 0.4

The sum of 2 consecutive odd integers is 204. What are the two odd integers?

Answers

101 and 104 i think is the most easy answer

Answer:

101, 103

Step-by-step explanation:

Say n is the first odd integer. The sum of n and its consecutive integer can be written as n + (n + 2). Doing some simple algebra:

n + (n+2) =204

2n + 2 = 204

2n = 202

n = 101

n is 101, and its consecutive integer, (n+2), is 103.

Owen bought 7 pounds of bananas for
$8.75. Olive bought 10 pounds of
grapes for $12. How much lower was
Olive's unit rate than Owen's unit rate?

Answers

Answer:

$0.05/lb

Step-by-step explanation:

What Owen paid, per pound: ($8.75) / (7 lb) = $1.25/lb

What Olive paid, per pound: ($12) / (10 lb) = $1.20/lb

Olive's unit rate was $0.05/lb lower than Owen's.

Look at the table showing prices of orange juice.

Prices of Orange Juice
Pint (16 oz)
Quart (32 oz)
Half-Gallon (64 oz)
Gallon (128 oz)
$1.28
$1.92
$4.48
$11.52

Which is the best value for buying orange juice?
pint
quart
half-gallon
gallon

Answers

Answer:

B quart

Step-by-step explanation:

Answer:

the answer will be B quart

Step-by-step explanation:

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 (2025)

FAQs

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? ›

Expert-Verified Answer

How can you tell if f(x) and g(x) are inverse functions? ›

Inverse of a Function. Let f(x) and g(x) be two one-to-one functions. If (f∘g)(x)=x ( f ∘ g ) ( x ) = x and (g∘f)(x)=x ( g ∘ f ) ( x ) = x then we say that f(x) and g(x) are inverses of each other. We denote g(x) (the inverse of f(x) ) by g(x)=f−1(x).

How do you confirm that f and G are inverses by showing that? ›

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. As per the problem statement the condition that both functions are inverse of each other means the following: f(g(x)) = x and g(f(x)) = x.

Are f(x) and g(x) inverse functions if f(x) 2x 2 and g(x) 2x 2 give your answer as yes or no? ›

Final answer:

The functions f(x) = 2x + 2 and g(x) = -2x - 2 are not inverse functions.

Are f and g inverses of each other? ›

f andg are inverses when f(y)=x f ( y ) = x iffy=g(x). This is equivalent tof(g(x))=x f ( g ( x ) ) = x andg(f(y))=y, g ( f ( y ) ) = y , which can also be expressed as g(f(x))=x. g ( f ( x ) ) = x . suppose i'm saying one function gives answer y for x.

How to know if a function is an inverse of another? ›

Inverse functions: These types of functions can be created by switching the input and output variables in a function. If a function is inputted into another and you get an output of x, then we know these two functions are inverses of each other.

How to check if an inverse function is correct? ›

Given a function f(x), we can verify whether some other function g(x) is the inverse of f(x) by checking whether either g(f(x))=x or f(g(x))=x is true. We can test whichever equation is more convenient to work with because they are logically equivalent (that is, if one is true, then so is the other.)

How do you prove that f and G are inverse functions? ›

The inverse function returns the original value for which a function gave the output. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.

Does f x )= x have an inverse? ›

Since f−1(f(x))=x f - 1 ( f ( x ) ) = x and f(f−1(x))=x f ( f - 1 ( x ) ) = x , then f−1(x)=x f - 1 ( x ) = x is the inverse of f(x)=x f ( x ) = x .

What happens when FX and GX are inverse function of each other? ›

Concept: A function g is the inverse of a function f if whenever y = f(x) then x = g(y). We can write this in terms of the composition of f and g as g(f(x)) = x. -> The UPSC NDA 2 Admit Card has been released for the exam scheduled on 1st September 2024.

Which functions have inverses? ›

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.”

Why f does not have an inverse? ›

Since there is not a unique value for the input (x), we cannot define an inverse function for f ( x ) = x 2 . This example demonstrates that a many-to-one function, like f ( x ) = x 2 , does not have an inverse function because it does not meet the one-to-one condition required for inverse functions.

Are these two functions inverses? ›

To check if two functions are inverses, we evaluate both compositions. If f(g(x))=x and g(f(x))=x hold true for all values of x in the appropriate domains, we can conclude that the functions are indeed inverses.

Which statement verifies that f(x) and g(x) are inverses of each other? ›

Expert-Verified Answer

The correct statement verifying that f(x) and g(x) are inverses of each other is D. f(g(x))=x and g(f(x))=x. This means both functions undo each other, returning the original input x.

How do you determine algebraically whether f and G are inverse functions? ›

Two functions are inverses if the composition of the functions equals x. In other words, f and g are inverse functions if fog(x)=gof(x)=x. So, f and g are inverses.

How do you tell if a function is its own inverse? ›

When the graph of a function is known the graph of its inverse can be found by taking its mirror image along the line y=x. So if we get the mirror image of the function the same as the actual function then we can say that the inverse of this function is the same as the function.

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