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

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

Find the missing side. Round to the nearest tenth.

Answers

150 is your answer,hope it helped

Like what that guy said sorry did not mean to disturb

At age 21, Felipe is 60% of the minimum age he must be to become U.S. President.
What is the minimum age he must be to become U.S. President?

Answers

35 years of age
Hope this helped

Answer:

35 years

Step-by-step explanation:

[tex]\frac{60}{100} = \frac{21}{y}[/tex]

Cross Multiplying:

[tex]21*100 = 2,100\\2,100/60 = 35[/tex]

find the area of each shaded sector. Round to the nearest hundredths place. Use 3.14 for pi​

Answers

Answer:

8.48cm²

Step-by-step explanation:

area of a sector = [tex]\frac{0\pi r^2\\\\}{360}[/tex]

where 0 = angle measure of sector

and r = radius

we are given the angle measure ( 23° ) and the radius ( 6.5 cm )

so all we have to do is plug in the values into the formula

(Note that the question asks us to use 3.14 for pi)

[tex]A=\frac{23*3.14* 6.5^2\\\\}{360}\\6.5^2 = 45.25\\23*3.14 =72.22\\72.22*45.25 = 3051.295\\\frac{3051.295}{360} =8.47581944[/tex]

so the area of the sector = 8.47581944 cm^2

finally we want to round to the nearest hundredth and we get that the answer is 8.48cm²

What is the answer :>

Answers

um.. it’s just a black picture. :>

6
There are 20 sweets in a bag.
Seven of them are strawberry.
A sweet is taken at random from the bag.
What is the probability that the sweet taken is not strawberry?

Answers

7 of the sweets in the bag are strawberry. Since there are 20 sweets total in the bag, 20 - 7 = 13 sweets in the bag must be non-strawberry.

The probability that a sweet taken at random from the bag is not strawberry would thus be 13/20.

Your scores on the first 4 tests in Algebra were 85, 80, 90, and 93. What do you need to make on the 5th test to have a 90 average in the class?

Answers

Answer:

you would have to get a 100 on your fifth test

Step-by-step explanation:

because between your first 4 tests, the average is only 87 something but when you add 100 to that, the average turns to 89.6 which when rounded becomes 90.

2a+3b as a column vector

Answers

Answer:

Step-by-step explanation:

A submarine descends
300 meters in one hour.
What was it's average
change in depth per
minute?

Answers

Answer:

5 meters per minute

Step-by-step explanation:

300/60 = 5 meters per minute

BRAINLIEST FOR CORRECT ANSWER!
What is the transformation rule for a translation 3 units right?

Answers

Answer:Translation happens when we move the image without changing anything in it. ...

Rotation is when we rotate the image by a certain degree. ...

Reflection is when we flip the image along a line (the mirror line). ...

Dilation is when the size of an image is increased or decreased without changing its shape.

Please help I give brainliest

Answers

Answer:

Questions:

#1) one complex solution

#2) two solutions

#3) one complex solution

#4) one solution

Step-by-step explanation:

1) x² = -100;      x = 10i

2) 5x² = 1;         x = ±[tex]\sqrt{1/5}[/tex]

3) 6x² + 6 = 0;    x = i²

4) 7(x² + 6) - 42 = 0;    x = 0


The equation g=3r represents how much Trevin makes per hour at his job. What is the unit rate?​

Answers

Answer:

Hope It Help

Brainliest please

Answer:

3

Step-by-step explanation:

The unit rate is a rate with 1 in the denominator. The unit rate for this equation would be how much money he makes in one hour. So, to find the unit rate plugin 1 for r and solve for g. One times three (1*3) is equal to 3; therefore, that is the unit rate.

Si por 3 kilogramos de manzana se pagan $20. ¿Cuánto hay que pagar por 15 kilogramos?

Answers

PLEASE ANSWER BOTH AS FAST AS POSSIBLE PLEASE HELP HELP ILL MARK BRAINLEST!!!!!

Answer:

$100

Step-by-step explanation:

15÷3=5

20•5=100

Hope this helps

What is the perimeter of the rectangle whose vertices are at (6, 3), (−6, 3), (−6, −1), and (6, −1)?

Answers

Given:

The vertices of a rectangle are (6, 3), (−6, 3), (−6, −1), and (6, −1).

To find:

The perimeter of the rectangle.

Solution:

Distance formula:

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

Let the vertices of a rectangle are A(6, 3), B(−6, 3), C(−6, −1), and D(6, −1).

Using the distance formula, we get

[tex]AB=\sqrt{(-6-6)^2-(3-3)^2}[/tex]

[tex]AB=\sqrt{(-12)^2-(0)^2}[/tex]

[tex]AB=\sqrt{144}[/tex]

[tex]AB=12[/tex]

Similarly,

[tex]BC=\sqrt{\left(-6-\left(-6\right)\right)^2+\left(-1-3\right)^2}=4[/tex]

[tex]CD=\sqrt{\left(6-\left(-6\right)\right)^2+\left(-1-\left(-1\right)\right)^2}=12[/tex]

[tex]AD\sqrt{\left(6-6\right)^2+\left(-1-3\right)^2}=4[/tex]

Now, the perimeter of the rectangle is:

[tex]Perimeter=AB+BC+CD+AD[/tex]

[tex]Perimeter=12+4+12+4[/tex]

[tex]Perimeter=32[/tex]

Therefore, the perimeter of the rectangle is 32 units.

please help due todayyy://

Answers

Answer:

B. product graph

Step-by-step explanation:

Hope it helps

CarryOnLearning

PLEASE HURRY: On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75% of
the length it was on Monday.
Which of the following expressions could represent how many centimeters long Florencia's hair was after the
haircut?
Chose 2 answers:

h(1 - 0.75)

(1 - 75/100)h

3/4h

0.75h

1/4h

Answers

Answer:

It seems that you are trying to find the length of hair of Florencia on Tuesday.

Given that length of the hair of Florencia on Monday = h centimeters

On Tuesday, she got hair cut.

So new length of the hair of Florencia on Tuesday = 75% of Monday value

= 75% of (h)

= 0.75* (h)

= 0.75h

Hence final answer is the length of the hair of Florencia on Tuesday is ( 0.75h ) centimeters.

Answer:

3/4h and 0.75h

Step-by-step explanation:

khan

Given DE || BC, find the length of BD.

Answers

Answer:

BD = 12.5

Step-by-step explanation:

Full answer in the attachment!!

I suck at math
The math problem is below

Answers

Answer:

Brooklyn earns four more dollars than Anna does each hour.

Step-by-step explanation:

So basically in order to get the amount ech of them recieve you would have to divide. So for Anna's since her least given number is 10 hours you would divide how much she earns (256) by how many hours she has been working (10) and you get 25.6

Now for Brooke she is given only one piece of evidence so you would use that she has been working for 26 hours and earns 769.6. So divide her earning by the hour and get 29.6

Subtract each of the answers (29.6-25.6) and you would get 4

Sorry if it doesn't make sense I was trynna rush and give you the answer

Answer:

Brooklyn earns four more dollars than Anna does each hour.

Step-by-step explanation:

The area of the rectangle below is 18 square units and the length is 3 3/4 .What is the width of the rectangle?

Answers

Answer:4.8

Step-by-step explanation:18/3.75=4.8

Does this graph represent a function?

Answers

Yeas it does represent a function

would -60 be the opposite of 60?

Answers

Answer:

yes,please mark me brainlest

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

A negative number is the opposite of it's positive.

What is the perimiter of a quadrilateral with verticles at (5,2), (10,2), (5,5), and (10,5)

Answers

Answer:

55

Step-by-step explanation:

help me please!!! no links 10 points

Answers

in persectev i think the answer in bound to be 17/10

Answer:

x=3 y=13

Step-by-step explanation:

now you got x... substitute x value with one of the questions then you get y

-3×3+2y=17

-9+2y=17

2y=17+9

y=26/2

y=13

i hope it's clear this is how elimination method works... this is how i learned.... t☺️❤️

An estate valued at $60 000 is divided among
three daughters Annette, Betty and Carol in the
ratio 1:2:3 respectively.
(a) Calculate the amount each received.

Answers

Answer:34 13

Step-by-step explanation:

ffrff

20000 I divided 60,000 by 3 because there are three of them

Find the volume of the cylinder. Round your answer to the nearest hundredth.

Answers

9514 1404 393

Answer:

  1763.01 m³

Step-by-step explanation:

The height of the cylinder will be ...

  h = (18 m)sin(60°) = 9√3 m

The volume of the cylinder is ...

  V = Bh

where B is the area of the end circle.

  B = πr² = π(6 m)² = 36π m²

Then ...

  V = (36π m²)(9√3 m) ≈ 1763.01 m³

The volume of the cylinder is about 1763.01 m³.

The measures of the exterior angles of a hexagon are x°x°, 2x°2x°, 5x°5x°, 6x°6x°, 7x°7x°, and 9x°9x°. Solve for x.

Answers

Answer:

x = 12°

Step-by-step explanation:

The measures of the exterior angles of a hexagon are x°, 2x°, 5x°, 6x°, 7x°, and 9x°. Solve for x.

The sum of the exterior angles of a polygon sums up to 360

An hexagon is a 6 - sided polygon

(x + 2x + 5x + 6x + 7x + 9x) = 360

30x = 360

Divide both sides by 30

x = 360 / 30

x = 12

Hence, x = 12°

Help me with these questions​

Answers

Answer:

A is the correct Answer

Step-by-step explanation:

hope that helps

Answer:

igual es lo mismo

Step-by-step explanation:

hope that help

Help! Plz thank you!!!!

Answers

Answer:

i do not see a picture or an image of what you need.

Step-by-step explanation:

hiii please help i’ll give brainliest:)

Answers

I’m pretty sure it’s A, because after the war the Greeks won and only about 192 people died. But is there a passage with this?

Somebody please help. this is quadratics
Solve each equation by taking square roots.
[tex]1.)6x^2=-90\\2.)b^2-4=-2\\3.)16x^2-7=-6\\4.)10p^2+9=239[/tex]

Answers

Answer:

1)

[tex]6x^2=-90\\x^2=-15\\\sqrt{x^2} =\sqrt{-15} \\x=i\sqrt{15} ,-i\sqrt{15}[/tex]

2)

[tex]b^2-4=-2\\b^2=2\\\sqrt{b^2} =\sqrt{2} \\b=\sqrt{2} ,-\sqrt{2}[/tex]

3)

[tex]16x^2-7=-6\\16x^2=1\\x^2=\frac{1}{16} \\\sqrt{x^2} =\sqrt{\frac{1}{16}} \\x=\frac{1}{4} ,-\frac{1}{4}[/tex]

4)

[tex]10p^2+9=239\\10p^2=230\\p^2=23\\\sqrt{p^2} =\sqrt{23} \\p=\sqrt{23},-\sqrt{23}[/tex]

BRAINLISRST AND EXTRA POINTS I NEEDS I HELP

A study found that a car
depreciates 12% per year. If the
car was purchased for $15,000, how
much is it worth after 4 years?

Answers

Answer:

7800

Step-by-step explanation: :)

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