Find the inverse of the following function.

Find The Inverse Of The Following Function.

Answers

Answer 1

For this case we must find the inverse of the following function:

[tex]f (x) = \sqrt [3] {x + 12}[/tex]

For this, we follow the steps below:

Replace f (x) with y:

[tex]y = \sqrt [3] {x + 12}[/tex]

We exchange the variables:

[tex]x = \sqrt [3] {y + 12}[/tex]

We solve the equation for "and":

[tex]\sqrt [3] {y + 12} = x[/tex]

We raise both sides of the equation to the cube to eliminate the root:

[tex](\sqrt [3] {y + 12}) = x ^ 3\\y + 12 = x ^ 3[/tex]

We subtract 12 on both sides of the equation:

[tex]y = x ^ 3-12[/tex]

Thus, the inverse function is:

[tex]f ^ {- 1} = x ^ 3-12[/tex]

Answer:

Option B

Answer 2
Answer:

Option: B is the correct answer.

       B.    [tex]f^{-1}(x)=x^3-12[/tex]

Step-by-step explanation:

The inverse function f(x) is calculated in the following steps.

Put  f(x)=yInterchange x and y in the equation.Now, solve for y.

The function f(x) is given by:

[tex]f(x)=\sqrt[3]{x+12}[/tex]

Now, we keep:

[tex]f(x)=y\\\\i.e.\\\\y=\sqrt[3]{x+12}[/tex]

Now, we interchange x and y

[tex]x=\sqrt[3]{y+12}[/tex]

Now, on taking cube on both side of the equation we have:

[tex]y+12=x^3\\\\i.e.\\\\y=x^3-12[/tex]

i.e.

[tex]f^{-1}(x)=x^3-12[/tex]


Related Questions

What is the missing reason in the proof?

Answers

Answer:

Try A or D

Step-by-step explanation:

I did this last semester (I know my age is 32 I didn't know if you had to be over 18 or 21 so I guessed a year and aimed a little to high...) I think it is either A or D

Answer:

Its A (APEX)

Step-by-step explanation:

The Valdez family left at noon for a 4-hour trip to visit relatives. They stopped 1 hour for lunch and 2 hours to visit an amusement park. What time did they get to their relatives' house?

Answers

Answer:

7pm

Step-by-step explanation:

Noon means 12:00pm

Just add 3 hours to their originally 4 hour trip

(1 hour from lunch and 2 from the amusement park)

Answer:

7

Step-by-step explanation:

Can someone pls help me with my math problem will give brainliest if correct!

Answers

37 over 8 or 37/8. I plugged it in on my calculator and it was correct.

Answer:

37 over 8 or 37/8 or 37:8 or[tex]\frac{37}{8}[/tex]

Step-by-step explanation:

1) A number is chosen at random from 1 to 25. Find the probability of not selecting
a prime number.
) A number is chosen at random from 1 to 25. Find the probability of selecting
a prime number.

Answers

Answer:

Prime: 9/25    Not Prime: 16/25

Step-by-step explanation:

In 1 - 25 there are 9 prime numbers, or numbers that cannot be divided by anything other than 1 or itself. They are  2 3 5 7 11 13 17 19 and 23,

Selecting a NON Prime: 25-9= 16 so we would put 16 over 25.

16/25 since it can not be reduced that is the fraction

Selecting a Prime: We know there is 9 prime numbers so we would put it over 25. 9/25 also cannot be reduced any further,

what is the formula for area of a triangle

Answers

Answer:

A = [tex]\frac{1}{2}[/tex]bh

Step-by-step explanation:

The area of a triangle is defined as half the product of its base by its height.

A = [tex]\frac{1}{2}[/tex]bh

If you do not know the height but you know the length of the three sides of the triangle you can use Heron's formula to find the area

If the lengths of the sides are a, b, c then the area is

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where

[tex]s =\frac{a+b+c}{2}[/tex]

You do length x width (for triangles its called base x height) and divide the product by 2

Find the measure of a central angle of a regular polygon with 10 sides

Answers

Answer:

114 degrees

Step-by-step explanation:

The formula to find the measure of all angles in a regular polygon is [tex](n-2)180[/tex], where n = total number of sides.

Thus, we substitute n for 10, and you get:

[tex](10-2)180=1440[/tex]

If the shape is a regular polygon and it has ten sides, meaning all sides are equal, then all you do is divide 1440 by 10, to get the final answer of 114.

A central angle in a regular ten-sided polygon would be 144 degrees.

Final answer:

The central angle of a regular polygon with 10 sides (a decagon) is calculated by dividing 360° by the number of sides, resulting in a central angle of 36°.

Explanation:

To find the measure of a central angle of a regular polygon with 10 sides (a decagon), we use the formula for the measure of each central angle:

Central Angle = 360° / Number of sides

Thus, the central angle of a regular decagon is:

360° / 10 = 36°

This is because the central angles are equally distributed around the center point, dividing the 360° of a circle evenly by the number of sides in the polygon.

a car travels 30 1/5 miles in 2/5 of an a hour. what if the average speed, in miles, per hour of the car?

Answers

Answer:

Average speed = 30.2 miles / .4 hours =

75.5 mph

Step-by-step explanation:

Answer:

Average speed of the car is [tex]75.5\text{ miles per hour}[/tex].      

Step-by-step explanation:

We are given the following information:

Distance traveled by the car =

[tex]30\displaystyle\frac{1}{5}\text{ miles}[/tex]

Time taken by the car =

[tex]\displaystyle\frac{2}{5}\text{ hours}[/tex]

Formula:

Speed = [tex]\displaystyle\frac{\text{Distance covered}}{\text{Time taken}}[/tex]

Putting all the values,

[tex]\text{Speed} = \displaystyle\frac{30\frac{1}{5}}{\frac{2}{5}} = \frac{\frac{151}{5}}{\frac{2}{5}} = \frac{151}{2} = 75.5\text{ miles per hour}[/tex]

Average speed of the car is [tex]75.5\text{ miles per hour}[/tex].

how do you work out 12÷6×2-2²

Answers

For this case we must use the order of algebraic operations according to the PEMDAS method:

P: Parentesis

E: Exponential

MD: Multiplication and division from left to right

AS: Addition and subtraction from left to right

We have:

12÷6×2-[tex]2 ^ 2[/tex] =

12÷6×2-4 =

2×2-4 =

4-4 =

0

Answer:

0

Answer:

0

Step-by-step explanation:

Lesson: Order of operations

PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do exponent first.

12÷6*2-2²

2²=2×2=4

12÷6×2-4

Multiply and divide from left to right.

12÷6×2

12÷6=2

2×2=4

4-4

Subtract from left to right.

4-4=0

0 is the correct answers.

I hope this helps you, and have a wonderful day!

The product of two whole numbers is 180 and their sum is36. What are the two numbers?

Answers

Answer:

6,30

Step-by-step explanation:

The product of two whole numbers is 180

xy = 180

and their sum is 36

x+y = 36

x = 36-y

Substitute this into the first equation

(36-y) (y) = 180

36y - y^2 = 180

Add y^2 to each side

36y = 180 +y^2

Subtract 36y from each side

0 = y^2 -36y +180

Factor

0=(y-6) (y-30)

Using the zero product property

y-6 =0   y-30 =0

y = 6    y= 30

Now we need to find x

If y =6

x = 36-6=30

If y = 30

x = 36-30=6

The two numbers are 30 and 6

What is the solution to the system of equations y = -x - 5 and y = 2x + 4

Answers

Answer:

(-3,-2)

Step-by-step explanation:

y = -x - 5

y = 2x + 4

plug in one of the y equations

(2x+4)= -x - 5

2x+4=-x-5

3x=-9

x= -3

plug in x to one of the y equations

y= -(-3) -5

y=3-5

y= -2

x= -3, y= -2

Is the distributive property used to help simplify math expressions

Answers

Answer:

yes,its one way to simplify equations.

Step-by-step explanation:

A preschool playground has both bicycles and tricycles. There is a total of 30 seats and 70 wheels. how many bicycles are there? how many tricycles are there? ​

Answers

Answer:

20 bicycles and 10 tricycles.

Step-by-step explanation:

Let the number of bicycles and tricycles be x and y respectively.

Each vehicle has 1 seat.  Each bicycle 2 wheels and each tricycle 3 wheels.

Then we have the system of equations:

x + y = 30 ............ (1)

2x + 3y = 70.........(2)

Multiply the first equation by -2:

-2x - 2y = -60......(3)

Adding (2) + (3):

y = 10

Substituting for y in equation (1):

x + 10 = 30

x = 20.    

By simultaneous equation, there are a total of 20 bicycles and 10 tricycles.

What is the number of given quantity from simultaneous equation ?

Let the number of bicycles and tricycles be x and y respectively.

It is given that there is a total of 30 seats and 70 wheels.

Each vehicle has 1 seat.  Each bicycle 2 wheels and each tricycle 3 wheels.

Then we have the system of simultaneous equations:-

x + y = 30 ............ (1)

2x + 3y = 70.........(2)

Multiply the first equation by -2:

-2x - 2y = -60......(3)

Adding (2) + (3):

y = 10

Substituting for y in equation (1):

x + 10 = 30

x = 20.    

Therefore, by simultaneous equation, there are a total of 20 bicycles and 10 tricycles.

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What is the volume of the cylinder below

Answers

Answer: D)

Step-by-step explanation: this is because you find the area of the circle which is pi times radius squares. So the area of the circle is 16 pi. And the. You have to multiply by 7 because you are staking the circle 7 times. To get 122 pi which is the answer so the answer is D. :)

The value of the volume of the cylinder is,

V = 96π units³

What is cylinder?

A cylinder is a three-dimensional solid that maintains, at a given distance, two parallel bases connected by a curved surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centres of the two bases.

We have to given that;

Radius of cylinder = 4 units

Height of cylinder = 6 units

Since, The value of volume of cylinder is,

⇒ V = πr²h

Hence. The value of the volume of the cylinder is,

V = π (4²) × 6

V = 16 × 6 π

V = 96π units³

Thus, The value of the volume of the cylinder is,

V = 96π units³

To learn more about cylinder visit:

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A bicyclist covered 5/7 of his route and an additional 40 miles. He has yet to cover 118 miles less than 0.75 of his route. How long is his route in miles?

Answers

Answer:

168 miles.

Step-by-step explanation:

5/7x+40+0.75x−118=x

Step 1: Simplify both sides of the equation.

5/7x+40+0.75x−118=x

5/7x+40+0.75x+−118=x

(5/7x+0.75x)+(40+−118)=x(Combine Like Terms)

1.464286x+−78=x

1.464286x−78=x

Step 2: Subtract x from both sides.

1.464286x−78−x=x−x

0.464286x−78=0

Step 3: Add 78 to both sides.

0.464286x−78+78=0+78

0.464286x=78

Step 4: Divide both sides by 0.464286.

0.464286x/0.464286=78/0.464286

x=168

Final answer:

The total length of the bicyclist's route is 560 miles. This is solved by setting up an equation based on the given information and solving for the total route length.

Explanation:

To solve this problem, we first need to represent the problem using equations by setting X as the total route. We know that the bicyclist has already covered 5/7 of his route and an additional 40 miles. So, the part of his route he has already covered is expressed as [tex](5/7)X + 40.[/tex]

We also know that he has yet to cover 118 miles less than 0.75 of his route, so the part of the route that he has yet to cover is expressed as 0.75X - 118. Since the parts of the route already covered and yet to be covered add up to be his entire route (X), we can set up the equation as follows: ([tex](5/7)X + 40 = 0.75X - 118[/tex]. By solving this equation, we find that X (the total length of his route) equals 560 miles.

Learn more about Algebra here:

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What is the area of this trapezoid 6m 5m 3m 1m

Answers

The answer depends on which measure is the height and both bases.

someone plz help me​

Answers

Answer:Which one do you need help with

Step-by-step explanation:

1. 5 Folder 5 Pen = yes

6 Pen 6 Eraser = Yes

1 Pen 4 Notebook = No

3 Folder 7 Eraser = No

4 Folder 2 Notebook = Yes

HELP ASAP
Explain how to create a graph to model the relationship between the 2 quantities in the table.
please write the answer

Answers

Step-by-step explanation:

the x (hours) is the x axis and the d (dollars) is the y axis. On the x axis count by 1's and on the y axis count by 25's. To plot each point go to hour and then dollars.

Answer:

Use the values in the table to create ordered pairs. Label the x-axis with the independent variable, hours. Label the y-axis with the dependent variable, dollars. Plot the ordered pairs on the graph. If the variables can be represented as fractional parts you can draw a line from the origin that connects the points.

Step-by-step explanation:

sample response

What is the value of z in the equation 2(4z -9 -7) = 166 -46?

A. 19
B. 21
C. 26
D. 34

10 points for the answer.

Answers

Answer:

A. 19

Step-by-step explanation:

2(4z -9 -7) = 166 -46

First combine like terms

2(4z -16) = 120

Divide each side by 2

2/2(4z -16) = 120/2

4z-16=60

Add 16 to each side

4z-16+16 = 60+16

4z = 76

Divide each side by 4

4z/4 = 76/4

z = 19

A team of runners ran a relay race. Each runner ran 7 1/2 kilometers. The total length of the race was 45 kilometers. Write and solve an equation to find how many runners were on the team. *

Answers

Answer:

6 runners

Step-by-step explanation:

Each runner ran 7.5 km.  If there were n runners, then (7.5 km)n = 45 km.

Solve this for n by dividing 7.5 km into 45 km:

n = 6

There were 6 runners.

Given the system of linear equations.

-x + y = 5, 4x + y = 10

Answers

Answer:

x = 1 and y = 6

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}-x+y=5\\4x+y=10&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-x+y=5\\-4x-y=-10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-5x=-5\qquad\text{divide both sides by (-5)}\\.\qquad x=1\\\\\text{put the value of x to the first equation}\\-1+y=5\qquad\text{add 1 to both sides}\\y=6[/tex]

evaluate the following expression 5(1 3)-3(2 -1)

Answers

The equation 5(1 + 3) - 3(2 - 1) when solved gives the final result 17.

To evaluate the expression 5(1 + 3) - 3(2 - 1), you need to follow the proper order of operations, which consists of parentheses first, then multiplication or division (from left to right), and finally addition or subtraction (also from left to right).

First, simplify the expressions inside the parentheses:

(1 + 3) = 4(2 - 1) = 1

Next, multiply each result by the number outside the parentheses:

5(4) = 203(1) = 3

Now subtract the second result from the first:

20 - 3 = 17

The evaluated expression is 17.

Consider a triangle A B C
like the one below. Suppose that
, C= 105 a=67 b=37
, and
. (The figure is not drawn to scale.) Solve the triangle. A B C are on the points of the triangle
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.

If there is more than one solution, use the button labeled "or".
c= A= B=

Answers

Answer:

sorry, that is a very complex question

Step-by-step explanation:

it had to be more tjan 20 characters

What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.​

Answers

sin x = 32/58

We need to find the angle x.

Take the sine inverse on both sides.

Let arcsin = sine inverse

arcsin(sin x) = arcsin(32/58)

x = 33.485376623

Rounding off to the nearest hundredth, we get x = 33.49°.

Done!

Answer:

33.49

Step-by-step explanation:

I took the test

how many solutions does -3x+7=3x+7​

Answers

I think it's either 21+4×6-1=9 or 2+6×8-6=7

Answer:

One solution

Step-by-step explanation:

Adding 3x to both sides results in   7 = 6x + 7, or 6x = 0.  There is one solution, and that solution is x = 0.

What value makes this equation true? 4x-3=0?

Answers

Answer:

x = 3/4

Step-by-step explanation:

4x-3=0

Add 3 to each side

4x-3+3 = 0+3

4x = 3

Divide each side by 4

4x/4 = 3/4

x = 3/4

Answer: X = 3/4

Solution:

Move the constant to the right side and change its sign, then divide both sides by four:

4x - 3 = 0 --> 4x = 3 --> (4x/4) = (3/4)

X = 3/4

Please help me! WILL MARK BRAINLIEST. Thanks!

Answers

Answer:

For the first table: (0, 10) (1, 15) (2, 20) (3, 25) (4, 30)

For the second table: (-2, 1.04) (-1, 1.2) (0, 2) (1, 6) (2, 26)

For the third table: (-2, 10) (-1, 0) (-1/2, -5/4) (1, 10)

Step-by-step explanation:

There are 25 students in Mrs. Venetozzi’s class at the beginning of the school year, and the average number of siblings for each student is 3. A new student with 8 siblings joins the class in November.

Answers

Adding the student with eight siblings will increase the class average amount of siblings because this student has more siblings than the average.

The new class average for number of siblings is 3.19

Therefore, the average number of siblings that each student has is larger than the original average.

Answer:

The average will go up.

Step-by-step explanation:

Find the solution to the equation -2(x + 5) = -16. x =

Answers

Answer:

x = 5/7 = 0.714

Step-by-step explanation:

Answer is 5/7 = 0.714

See photo

solve by factoring:
5t=t ^2

Answers

Answer:

t=0 and t=5

Step-by-step explanation:

5t = t^2

Subtract 5t from each side

5t-5t = t^2 -5t

0= t^2 -5t

Factor out a t

0= t(t-5)

Using the zero product property

t=0  and t-5 =0

t=0  and  t-5+5=0+5

t=0 and t=5

Six is subtracted from a number the result is divided by four this result is added to 10 to give 30 what is the number

Answers

let's say the number is X and the result is YX-6=Yy/4+10=30y=(30-10)x4=80so X=80+6=86

Answer: The number is 86.

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

"Six subtracted from a number ", a number means the variable (x), and six subtracted from a number is "x -6".

"The result is divided by 4", so (x-6) /4.

This result is added to then, so: 10+ (x-6) /4.

And finally, to give 30 means that all the expression equals to 30.

10+ (x-6) /4 = 30

Solving:

(X-6) /4 = 30 -10

(X-6) /4 = 20

X-6 = 20x4

X-6 = 80

x =80+6

x= 86

The number is 86.

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