PLEASE HELP A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions using interval notation.

PLEASE HELP A. Use Composition To Prove Whether Or Not The Functions Are Inverses Of Each Other. B. Express

Answers

Answer 1

Answer:

Part A : see composition process below

Part B :    [tex]Domain=\{x\,|\,x\neq 0\}[/tex]

Step-by-step explanation:

Part A

Let's use the composition of functions to find if they give the identity : [tex]f(g(x))=x[/tex]  thus proving they are the inverses of each other:

[tex]f(g(x))=f(\frac{5x+1}{x} )=\frac{1}{\frac{5x+1}{x}-5} =\frac{1}{\frac{5x+1-5x}{x}} =\frac{1}{\frac{1}{x} } =x[/tex]

So we have proved they are the inverses of each other.

Part B

Given that the composition is:

[tex]f(g(x))=\frac{1}{\frac{1}{x} }[/tex]

the Domain must exclude x=0, for which this quotient is undefined.

The Domain is then:

[tex]Domain=\{x\,|\,x\neq 0\}[/tex]


Related Questions

PLEASE HELP! Will mark brainliest! Find the slope of the line:

Answers

Answer:

Step-by-step explanation:

I think 3-y slope

I will rate 5 stars to anyone who answers first. A number cube is rolled. What is the probability that a number greater than 4 will be rolled? (5/6), (1/3), (2/3) (1/6).

Answers

1/3 because i took the test and it was right

Answer:1/3

Step-by-step explanation:

There are 6 sides and 2 numbers more than 4

Put that info into a fraction 2/6

Then simplify 1/3

HELP QUICK!
A parabola, (y + 2)2 = 8(x - 3), is changed to (y + 10)2 = 8(x - 3). How will this affect the graph of the parabola?
A)
The vertex will shift up.
B)
The vertex will shift down.
C)
The vertex will shift to the left.
D)
The vertex will shift to the right.

Answers

Answer:

B) The vertex will shift down.

Step-by-step explanation:

In the equation of a parabola, (y - k)² = 4p(x - h), (h, k) is the vertex.

The original parabola's vertex was (3, -2).

In the new parabola, the y-coordinate changed to -10, making the new vertex (3, -10).

So, the parabola's vertex shifted down 8 units from -2 to -10.

The answer is To this question is B

what is the value of x

Answers

Answer:

x = 78

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

Answer:

78 degrees

Step-by-step explanation:

According to vertical angles theorem (vertical angles, angles that are opposite to each other and formed by two intersecting straight lines, are congruent) 78 and x are congruent

Change 06:00 to 12 hour clock time using a.m. and p.m.
I will mark you as brainlist

Answers

Answer:

06:00 a.m.

Step-by-step explanation:

That very simble, from 0:00 to 11:59 you use am, from 12:00 to 23:59 you use p.m :)

YOUR ANSWER WOULD BE 6:00AM!!!!!!

Michael just drank a cup of coffee to help him stay awake. The coffee had 110 milligrams of caffeine in it. If his body processes 5% of the caffeine every hour, how much will be left in 8 hours? A.74 B.72 C.56 D.73

Answers

Answer:C

Step-by-step explanation:

Answer C.56!

%5 of 110 is 5.5, 5.5 • 8= 54, 110-54= 56!

Find the number set which satisfies each of the problems. If 7 is subtracted from the absolute value of the sum of a number and 6, the result is 3.

Answers

Answer:

x=4      or    x= - 16

Step-by-step explanation:

|x+6|

Now subtract 7 which equals to 3.

|x+6|-7=3

|x+6|=10

Now remove the mode by adding plus minus sign in the front of 10.

x+6=±10

x+6=10 or x+6=-10

x=4      or x=-16

It is 4 or 16 you can put either one

PLEASE HELP!! URGENT

A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° Use the
information provided and the diagram below to determine the height of the tree. Round to the nearest
whole foot.
532 it
256 ft
479 ft
231 ft
13672 ft
< Previous
Next >

Answers

Answer:

The answer is option 1.

Step-by-step explanation:

You have to apply Tangent Rule, tanθ = opposite/adjacent. Then, you have to substitute the following values into the formula :

[tex]tan(θ) = \frac{oppo.}{adj.} [/tex]

[tex]let \: θ = 25.7 \: , \: oppo. = h \: , \: adj. = 532[/tex]

[tex] \tan(25.7) = \frac{h}{532} [/tex]

[tex]532 \tan(25.7) = h[/tex]

[tex]h = 256 \: feet \: (3s.f)[/tex]

The value of height of tree is,

⇒ h = 256 feet

We have to given that,

A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° .

Hence, By given figure we get;

By using trigonometry formula, we get;

⇒ tan 25.7° = Opposite / Adjacent

⇒ tan 25.7° = h / 532

⇒ 0.4812 = h / 532

⇒ h = 0.4812 × 532

⇒ h = 256 feet

Therefore, The value of height of tree is,

⇒ h = 256 feet

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A rectangular prism has a volume of 285.6. cubic feet. The prism is 12 feet long and 3.4 feet wide. What is the height of the prism? A. 7 ft B. 15 ft C. 19 ft D. 22 ft Please include all work!!

Answers

Answer:

A. 7 ft

Step-by-step explanation:

Volume is Length * Width * Height

12 * 3.4 * Height = 285.6

285.6 / 12 = 23.8

23.8 / 3.4 = 7

It’s is 7 because if u multiply all the numbers together you get your product

If g(x) = 1 - ¾ x
find: -5g(4) - 1

Answers

Answer:

-5g(4) - 1 is 9

Step-by-step explanation:

[tex]g(x) = 1 - \frac{3}{4} x[/tex]

when x is 4:

[tex]g(4) = 1 - \frac{3}{4} \times 4 \\ = 1 - 3 \\ = - 2[/tex]

therefore:

[tex] - 5g(4) - 1 = - 5( - 2) - 1 \\ = 10 - 1 \\ = 9[/tex]

Answer:

9

Step-by-step explanation:

g(x) = 1 - ¾ x

-5g(4) - 1

First find g(4) = 1 - 3/4(4) = 1 - 3 = -2

Then -5(-2) -1 = 10 -1 = 9

colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answers

Answer: 24

Step-by-step explanation:

Colleen painted 7 windows, some of which were her mother's.

Her dad painted 7+1 (8) windows, and that is twice as much as what her mother was supposed to do. Her mother was supposed to do 4 windows. That means Colleen's share was 3 windows.

If all the kids had to do an equal amount of windows, than each kid had to do 3 windows.

8+7+3+3+3=24

The total windows in the house are 21.

What is an algebraic expression?

It is an expression contains a relation between different parameters (variables). It contains variable and constant values, along with algebraic operations.

In our given problem, the algebraic relation between different members work output and total windows can be expressed as:

Windows painted by colleen and her mother = 7

Windows painted by father = (Windows painted by colleen and her mother + 1)

                                          = (7 + 1) = 8

∴ Windows painted by father = 8

Now, as given,

2 Windows painted by mother = Windows painted by father

∴ Windows painted by mother = [tex]\frac{8}{2}[/tex] = 4

and Windows painted by colleen = 7 - 4 = 3

Colleen and her 2 brothers paint equal windows;

∴  They painted 3 windows each.

The total windows in the house is equal to total painted windows by mother, father, colleen and her two brothers:

⇒ 4 + 8 + 3 x 3 = 12 + 9 = 21

Hence the total windows in the house are 21.

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Joseph said that a rhombus with side lengths of 6 meters and a height of 4 meters has the same area as a parallelogram with a base of 12 meters and a height of 2 meters. Is he correct? Critique Joseph's reasoning. help plzz​

Answers

Answer:

Area(s) of both rhombus and parallelogram are equal at 24 meters squared. Therefore Joseph had the correct reasoning in regards to area(s) of both rhombus and parallelogram are equal at 24 meters squared.

Step-by-step explanation:

To equate area of the rhombus, multiply the side length and height of rhombus in meters. (6 meters×4 meters=Area of 24 m°2). Area of parallelogram = (12meters ×2 meters= 24 m°2. Area(s) of both rhombus and parallelogram are equal at 24 meters squared. therefore

He was not correct because well… it’s obvious

11. In a box-and-whisker plot, the interquartile
range is a measure of the spread of the
middle half of the data. Find the interquartile
range for the data set: 10, 3, 7, 6, 9, 12, 13.
A 12
© 6
B 7
D 8

Answers

The answer to the question would be 6 because it’s in the middle
6. The range is the middle number in a sequence. That’s how you will find your awsner. You are welcome:)

The table represents linear function F

Answers

Answer:

D

Step-by-step explanation:

First we need to find the rate of change of function F. Function F have a slope/rate of change of (24-18)/(6-4)=6/2=3. Next we compute the slope/rate of change of Function G which is 4. Hence D is the answer

i’m just tryna ask my own question

A fortnight is 1/26 of a year. What part of a year is 8 fortnights?

Answers

Answer:

Isn’t it just 8/26

Step-by-step explanation:

Since 1 is 1/26 so 8 is just 8/26?

The part of a year is 8 fortnights is ( 8 / 26 ).

What is multiplication?

Multiplication is the process of determining the product of two or more numbers in mathematics.

It is given that a fortnight is 1/26 of a year. The part of the year for 8 fortnights is calculated as:-

⇒ 8 x ( 1 / 26 )

⇒( 8 / 26 )

Therefore, the part of a year is 8 fortnights is ( 8 / 26 ).

To know more about multiplication follow

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please help!!! ive been trying this question for the pass 20 minutes and cant seem to understand it!!

Answers

Answer:

D

Step-by-step explanation:

Beacuse ‍♀️

Answer:

This is a rectangle, so if AB is equal to 3 centimeters, then DC is equal to 3 centimeters.

Since Angle X is equal to 45 degrees, then angle CDE, is also equal to 45 degrees, and we have an isosceles triangle, since angle  CDE and DEC are equal to each other.

This means, that CE = DC.

And because E is the midpoint of CB, CE = EB.

So basically, we have:

DC = CE = BE

DC = 3

3 = CE = BE

And we see that CE and BE are both equal to 3, which makes CB equal to 6, which makes solving the area easy. (3 x 6), which is 18.

B is correct!

PLEASE HELP! I need this answered ASAP ;-; (Question is shown below in the attachment)

Answers

Answer:

3.14 units²

Step-by-step explanation:

The key realization here is that this shape is one quarter of a circle.

Therefore, it's area will be [tex]\frac{1}{4}[/tex] of the whole circle's area.

So, let's first find the area as if this were a whole circle.

The formula is [tex]\pi r^2[/tex], and we know that the radius, r, is 2. So:

[tex]\pi\cdot2^2\\\\\pi\cdot4\\\\3.14\cdot4\\\\12.56[/tex]

Now we need to find one fourth of this, we can do this by dividing by 4.

[tex]12.56\div4=3.14[/tex]

Hope this helped!

Answer:

pi units squared

Step-by-step explanation:

(cant find pi sign)

(pi times r^2)/4

4pi/4

pi

Find the length of KE. A. 30 B. 28 C. 15 D. 3

Answers

Answer:

28

Step-by-step explanation:

What value of p makes both sides equal the same? P = 3

37 - 9 = 28

21 + 7 = 28

So line KE and BE both equal 28

Hope this helps, and have a good day :)!

The length line KE and BE both equal 28.

Option (B) is correct.

Find the length of KE.

What is angle?

Figure which is formed by two rays or lines that shares a common endpoint.

Given that:

Let the value of

P = 3

Put the value of P

37 - 9 = 28

21 + 7 = 28

So, line KE and BE both equal 28

Learn more about angle here:

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Find the surface area and volume of the following figures.

Answers

White figure Area = 128[tex]\pi[/tex]

White surface area = appro. 301

Yellow area = 320[tex]\pi[/tex]

Yellow Surface area = approx. 653

Area found with = 2πrh+2πr2

Surface Area found with = 2πrh+2πr2

You need to memorize them for tests

Hope that helped!!! k

There a hinded message Jeff

22% of $900 = twenty two percent of $900 =

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

$198

▹ Step-by-Step Explanation

[tex]\frac{22}{100} * 900\\\\\frac{22}{1} * 9 = \frac{198}{1} \\\\= 198[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

198

Step-by-step explanation:

22% of 900

22% * 900

Change to decimal form

.22 * 900

198

Sala earns 12 dollars each hour working part-time at a bookstore. She earns one additional dollar for each book that she sells. Let A be the amount (in dollars) that Salma earns in an hour if she sells B books. Write an equation relating A to B. Then graph your equation using the axes below.

Answers

Answer:

y=12a+b

Step-by-step explanation:

answer: y=12a+b :))))

PLEASE HELP ME!!!!!!!!!!

Answers

Answer:

5:

x = 9  y = 34

x = 2  y = 6

x = -6  y = -26

x = 3  y = 10

x = 4  y = 14

6.

x = 8  y = 19

x = 5  y = 35

x = -2  y = -21

x = 1  y = 3

x = 4  y = 27

1.

x = 2  y = -5

x = 5  y = -2

x = -1  y = -8

x = 7  y = 0

x = 3  y = -4

2.

x = 8  y = 5

x = 2  y = -1

x = -2  y = -5

x = 9  y = 6

x = 1  y = -2

3.

x = 3  y = -1

x = 6  y = 2

x = -7  y = -11

x = 4  y = 0

x = 2  y = -2

4.

x = 6  y = 39

x = 5  y = 32

x = -9  y = -60

x = 1  y = 4

x = 2  y = 11

5.              6.             1.            2.         3.          4.

x  | y      |       x | y        x | y       x | y      x | y      x | y

9 | 11      |       3 | 19      2 | -5     8 | 5     3 | -1     6 | 39

2 | 6      |       5 | 35     5 | -2     2 | -1     6 | 2     5 | 32

-6| -26  |      -2 | -21    -1 | -8     -2 | -5   -7 | -11  -9 | -66

3 | 10    |        1  | 3       7 | 0       9 | 6     4 | 0      1 | 4

4 | 14    |        4 | 27     3 | -4       1 | -2    2 | -2    2 | 11

Hope this helps!

attachment help for question c no explanation only answer thank you

Answers

Answer:

Tablets.

Step-by-step explanation:

You didn't want an explanation so....here you go....no explanation.

Hope that helps and maybe earns a brainliest.

Have a great day!

the answer is

tablets

Find the area of the figure in the image attached. Round to the nearest tenth if necessary.

Answers

829 multiply all the outside numbers
It’s 829 hopefully this helps

help i want help i want help

Answers

Answer:

[tex] \boxed{127 \: {in}^{2} }[/tex]

Option A is the correct option.

Step-by-step explanation:

Surface area of the rectangle base = 9 × 5 = 45 in²

Surface area of lateral square = ( 5 )² = 25 in²

Surface area of lateral rectangle = 6.4 × 5 = 32 in²

Surface area of top square = ( 5 )² = 25 in²

Surface area of two parallel trapezoids:

[tex] (\frac{1}{2} (9 + 5) \times 5) \times 2[/tex]

= 7 × 5 × 2

= 70 in²

Total surface area:

= 45 + 25 + 32 + 25 + 70

= 197 in²

Hope I helped!

Best regards!

great work from them^ , the person above me answered this correctly it is 197in ^2

A. ASA
B. CPCTC
C. AAS
D. SAS

Answers

Answer:

It is ASA congruence rule as the 2 angles and the included side of the triangle are equal

Answer: ASA

Explanation:

There are one side and 2 angles in the proof.

what expression is equivalent to this equation :
(-3x3y2)(5x5y4)2​

Answers

Answer:

The equivalent expression to this equation is -30x⁸4y⁶

Step-by-step explanation:

For this expression, we have to multiply the terms. We can do this by following the order of operations.

(-3x³y²)(5x⁵y⁴)2

First, we have to multiply -3x³y² and 5x⁵y⁴ together.

(-15x⁸2y⁶)2

Now, we  multiply these terms together.

-30x⁸4y⁶

So, the expression that is equivalent to this equation is -30x⁸4y⁶

Answer:

Step-by-step explanation:

Plssss answer this guys fastt Pleaseeee
Pleaseeeeeeeeeeeeeeeeeee
And when u make pls do it all and not half thanks u so much if u dooo

Answers

Answer:

You cant get someone to do all of this try doing a few or getting help from someone older that's what I did

Explanation:

I asked help for one problem and the explanation and now I understand how they did it so the other problems I can do now

It's better to make an effort and try doing some of them instead of asking someone to do all of it

Because when the test comes it won't be that easy so next time just try putting a few so that way you can try understanding it and you can apply it to similar problems.

I hope you can find this some what help to you in the future. Also this is a suggestion from my experience so you don't have to do it I'm just trying to help out.

A parrarel line can look like // or \\ or || or = they can not be angles to where if they kept going they would eventually meet or touch not sure if your teacher is that strict tho I suggest using a tiler

For question number 2 then just draw a line going through it then lable every corner there is 1 to 8 1 2 3 4 5 6 7 8

For questions 3-6 Draw a triangle
Place it in the different corners and describe what it looks like and if it covers each corner completly incomplete or covers more than just one corner that repeats untill question number 7

For number 7 you need to draw to spearate pictures with these pictures just label the onea inside of the triangle hence why they are called interior angles

Graph y = 2x + 2 * Make a table of ordered pairs

(photo attached)

Answers

2 Times + 2 =4 table of a pair
2x +2=4 table of a pair

Three-fourths of the water leaked out of a full aquarium tank. and 15 gallons of
water was left. After the leak was fixed, 10 gallons of water was added to the
aquarium tank.
4) How many gallons of water can the aquarium tank hold when it is full?
5) How full was the aquarium tank after the 10 gallons of water was added?
6) How much more water would have to be added to fill the aquarium tank?

Answers

Answer: 4) 60 gallons    5) 25 gallons    6) 35 gallons

Step-by-step explanation:

If three-fourths of the water in the tank leaked out of the full aquarium tank then one-fourths will be left.

so if the leftover was 15 gallons then 1/4 of a number has to equal 15 gallons.

We could represent that by the equation.

1/4 * x = 15

0.25x = 15

x=  60    

4) which means the aquarium tank can hold 60 gallons of water when it is full.

5) If 15 gallons of water was left after the leaking and then they added 10 more gallons of water then 15 + 10 = 25   which means the aquarium was 25 gallon full.

6) If they are 25 gallons in the water now and we need to add some amount of water to get to 60 gallons of water then we will subtract  25 from 60 find how much water needs to be added.

So  60 -25 = 35   which means 35  gallons needs to be added.  

Yup the guy above is right
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