Mathematics High School

Find f-1(x) if f(x) = 2x/3-4

Answers

Answer 1

Given:

The function is:

[tex]f(x)=\dfrac{2x}{3}-4[/tex]

To find:

The inverse of the given function, i.e., [tex]f^{-1}(x)[/tex].

Solution:

We have,

[tex]f(x)=\dfrac{2x}{3}-4[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=\dfrac{2x}{3}-4[/tex]

Step 2: Interchange x and y.

[tex]x=\dfrac{2y}{3}-4[/tex]

Step 3: Isolate y.

[tex]x+4=\dfrac{2y}{3}[/tex]

[tex]3(x+4)=2y[/tex]

[tex]\dfrac{3x+12}{2}=y[/tex]

[tex]\dfrac{3}{2}x+6=y[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex]

Therefore, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{3}{2}x+6[/tex].

Related Questions

What is the angle of rotation counterclockwise about the spinner’s center that maps label h to label A? 252° 324° 144° 216°

Answers

Answer:

its 324

Step-by-step explanation:

somebody answer i need Help

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Answer:

$5.00

Step-by-step explanation:

$5 because it occurs the most

Answer:

Step-by-step explanation:

The mode is the price that appears the most often in a given list.

Solve the equation above for x

Answers

Answer:

2/3x=1-2

X=-1*3/2

X=-3/2

So is - 3/2

Two six-sided number cubes are rolled at the same time. What is the probability that the result will have at least one two in it?
(A)7/36
(B)1/5
(C)11/36
(D)1/6

Answers

Answer:

1/6

Step-by-step explanation:

There are 12 numbers in total. There is a 2 on each cube so there are two possible chance. 2/12=1/6 2/2=1 and 12/2=6 therefore 2/12=1/6

The solution is, the probability that the result will have at least one two in it is, 1/6.

What is probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

Two six-sided number cubes are rolled at the same time.

so, we get,

There are 12 numbers in total.

There is a 2 on each cube so there are two possible chance.

2/12=1/6

2/2=1

and 12/2=6

now, we have,

therefore 2/12=1/6.

Hence, The solution is, the probability that the result will have at least one two in it is, 1/6.

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What is 9 006 in word

Answers

Answer: 9006 in word form is nine thousand six ,

I hope you find this helpful.

Answer: 9,006 in word-form is nine thousand six.

Explanation: To write a number in word form, simply type the number in word form like I did above. If a digit doesn't have a zero, don't type zero, just type the number like I did above. Notice how I didn't include the word "zero" in my answer.

Let me know of any questions or concerns.

A water pipe has a flow of 2 gallons per minute how many 2 qt could fill it in 1/2 hour?

Answers

Answer:

60 Gallons in 1/2 hour. So we can convert that to 240 quarts. it says 2 so we divide that by two. 240/2=120

Step-by-step explanation:

Hope this helps!

At a hockey game a vendor sold a combined total of 102 sodas and hot dogs the number of hot dogs sold are 50 less than the number of sodas sold find the number of sodas sold and the number of hot dogs sold

Answers

Answer:

26 hotdogs

76 sodas

Step-by-step explanation:

x - 50 for hot dogs

x for sodas

(x-50) + x = 102

2x -50 = 102

2x = 152

x = 76

76-50 = 26 hotdogs

76 sodas

Determine the value of x in the figure below:

A
43.23
B
.02
C
48.95
D
31.95

Answers

Answer:answer is D

Step-by-step explanation:

what is the mean of the data set below 2, 3, 5, 6, 6, 10, 15, 15,

Answers

6.5 is the mean of the data

Which describes a number that cannot be irrational?
a number that can be used to solve an algebraic equation
a number that represents the ratio of the circumference to the diameter of a circle
a number that represents the length of the diagonal of a square
a number that can be written as the ratio of two integers

Answers

1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez1+1=2 ez

Please help will give brainliest

Answers

Answer:

A) 18cm^2

Step-by-step explanation:

(3 x 12)/2=36/2=18

Answer:

Step-by-step explanation:

12x3=36/2=18

Can you answer 1 and 2

Answers

Answer:

You have them both correct. #1 is B #2 is C

Step-by-step explanation:

Will mark brainlest

Answers

Answer:

15)

Step-by-step explanation:

i think its that since im guessing that x5 is the length of each side and since triangles have 3 sides so i did 5 x 3 which equals 15

What is the value 8x=5x+21

Answers

x = 7

8(7) = 5(7) + 21

56 = 35 + 21

56 = 56

X=7 is the answer

8x=5X+21
8x-5x=21
3x=21
X=21/3
X=7

Please help links=report and if correct I’ll mark you brainiest

Answers

Answer:

A is the correct answer.

Hope this helps [tex]\mathtt{: )}[/tex]

Find two numbers that have a sum of -2 and a product of -48 (please show work if possible)

Answers

Answer: -8 and 6

Step-by-step explanation:

factors of 48: 1,2,4,6,8,12,24,48

1 x 48

2 x 24

4 x 12

6 x 8

for a negative product, one of the factors must be negative and the other positive.

for two number to have a sum of -2, the greater number must be the negative number, and both numbers should have be two values apart (ex. 6 and 8, 3 and 5, 12 and 14, etc.). In this case, 8 would have to be negative whereas 6 will be left positive.

and then we check:

-8 x 6 = 48

-8 + 6 = -2

Please answer these and don’t just type in random things so u can get the points , I wanted to give 50 but I don’t trust some of you with answering.

Answers

Answer:

2) 6,290

3) 13,540

Step-by-step explanation:

Formula for each question:

Amount of money made = Base salary + (Amount sold × Commission percentage)

17% = 0.17

0 + (37000 x 0.17)

6290

6% = 0.06

10000 + (59000 x 0.06)

10000 + 3540

13,540

Please help with this!

Answers

Answer:

1) 7:9

2) 343:729

3) 16:9

4) 64:27

5) 9:11

6) 81:121

A 25-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is one inch more than five times the length of the first piece. Find the lengths of the pieces.

Answers

Answer:

3 inch 6 inch 16 inch 3+6+16 = 25

Step-by-step explanation:

First piesce = F

Second piece = 2F

third piece = 5F+1

F + (2F) + (5F+1) = 25

8F +1 = 25

subtract 1 om both sides

8F = 24

divide both sides by 8

F= 3

3X2= 6

3X5 +1 = 16

What is the measure of an angle that is 3/6 of a circle?

Answers

Answer:

180 degrees

Step-by-step explanation:

A whole circle is 360 degrees and 3/6 of that (or 1/2) is 180 degrees. I hope this helps!

Eight figures are below. Which ones are polygons?

Type your answer as a list, separated by commas. For example, if you believe A, B, and C are polygons, type A, B, C.

Answers

Answer:

A,C,D is the answer

Answer:

C. is the answer................

Please help:(

A. D: (2, 1, 0, -2, -3), R (1, -3, -3, -3, -4}

B. D: (-3, -2, 0, 1, 2}, R: (-4, -3, 1)

C. D: (-3, -2, 1, 1, 2), R: (1, -3, -4)

D. D (-3, -2, 0, 1, 2), R (1, -3, -3, -3, -4)

Which is the answer?

Answers

Answer c would be the answer hope it helps

Step-by-step ex planation:

Plz help meeeeeeee I need help

Answers

Answer:

5.25 miles per hour

Step-by-step explanation:

2a+3b as a column vector

Answers

Answer:

Step-by-step explanation:

What is the answers to these.

Answers

Answer:

A）-28

B）-48

C）45

-28
-48
45!!!!!!!!

and that’s it !!

Kay feels that if she earns a profit of 40.00 at this craft, her business will be successful enough for her to branch out to other craft fairs. How many ornaments does she have to sale to earn a 40.00 profit. Write and solve an equation then explain how the steps and operations used in your algebraic solution compare to an arithmetic solution

Answers

6x-2.50x-30=40

3.50x-30=40

3.50x=70

x=20 ornaments

Kay has to sell 20 ornaments to get a profit of $40.00.

What is an Equation?

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Cost for the table = $30

Cost for each ornament = $2.50

Selling price of each ornament = $6.00

Profit = Revenue - Expense

Let x be the number of ornaments sold to get a profit of $40.00.

Revenue = 6x

Expense = 30 + 2.5x

6x - (30 + 2.5x) = 40

3.5x - 30 = 40

3.5x = 70

x = 20

Hence selling 20 ornaments would give Kay a profit of $40.00.

Learn more about Equations here :

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The complete question is as follows :

Kay's mother taught her how to make handmade ornaments to sell at a craft fair. Kay rented a table at the fair for $30 and set up her work station. Each ornament that she makes costs approximately $2.50 for materials. She sells each ornament for $6.00.

Kay feels that if she earns a profit of 40.00 at this craft, her business will be successful enough for her to branch out to other craft fairs. How many ornaments does she have to sale to earn a 40.00 profit. Write and solve an equation then explain how the steps and operations used in your algebraic solution compare to an arithmetic solution.

Consider a car rental for $42, plus $0.22 per mile driven. Which statements are correct?
A) This situation is modeled by a linear function.

B) If the car is driven 200 miles, the rental will cost $86.

C) If the car is driven 500 miles, the rental will cost $142.

D) This situation can be modeled by the function f(x) = 0.22x + 42.

E) This situation can be modeled by the function f(x) = (0.22)X + 42.

Answers

Answer:

a, b and d

Step-by-step explanation:

200 miles x 0.22 = 44$ + 42$= 86$

the equation would be f(x)= 0.22x + 42.

and its linear.

What is the value of the expression?

−5/12+7/34

Answers

-43/204

Step-by-step explanation:

−5/12 × 17/17 + 7/34 × 6/6 =

= −85/204 + 42/204

= −85 + 42/204

= −43/204

I forgotususjaajjajajaa

Find the CIRCUMFERENCE of a circle with the DIAMETER of 11 ft.
HELP PLS

Answers

Answer:

half of 11 is: 5.5

5.5 x 3.14 x 2 = 34.54

*EXTRA PTS* answer these pls :)

Answers

Answer:

3)x=7,y=-2

Step-by-step explanation:

Answer:

3, (7, -2)

4, no solution

Step-by-step explanation:

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