State the domain restriction(s) in interval notation of \displaystyle f\left(g\left(x\right)\right)f(g(x)) given: \displaystyle f\left(x\right)=\sqrt{3x-2}f(x)= 3x−2 ​ and \displaystyle g\left(x\right)=x-7g(x)=x−7

Answers

Answer 1

Answer:

The interval notation for the domain is [tex][\frac{23}{3},\infty ][/tex].

Step-by-step explanation:

Consider the provided information.

It is given that [tex]\:f\left(x\right)=\sqrt{3x-2},\:\text{ and }\:g\left(x\right)=x-7[/tex]

We need to find the value of [tex]f\left(g\left(x\right)\right)[/tex].

Put the value of g(x) in  [tex]f\left(g\left(x\right)\right)[/tex].

[tex]f\left(g\left(x\right)\right)=f(x-7)[/tex]  ....(1)

Now, put x=x-7 in [tex]\:f\left(x\right)=\sqrt{3x-2}[/tex]

[tex]\:f\left(x-7\right)= \sqrt{3(x-7)-2}[/tex]

[tex]\:f\left(x-7\right)= \sqrt{3x-21-2}[/tex]

[tex]\:f\left(x-7\right)= \sqrt{3x-23}[/tex]

From equation 1.

[tex]f\left(g\left(x\right)\right)=\:f\left(x-7\right)= \sqrt{3x-23}[/tex]

The domain of the function is the set of input values for which a function is defined.

Here, the value of [tex]3x-23[/tex] should be greater or equal to 0 as the square root of a negative number is not real.

Domain= [tex]3x-23\geq0[/tex]

[tex]x\geq\frac{23}{3}[/tex]

The value of x is all real number greater than [tex]\frac{23}{3}[/tex].

Hence, the interval notation for the domain is [tex][\frac{23}{3},\infty ][/tex].


Related Questions

PLEAS HELP I WILL GIVE 10 POINTS
ou are a high school senior with a part-time job at a retail store. Your employer pays you $9.75 per hour. Last week, you worked a total of 30 hours.

The following payroll deductions were taken from your gross pay:

Federal income tax (withholding) at 10%
Social Security tax at 6.2%
Medicare tax at 1.45%
Use the check stub below to help you think through the problem.

You are encouraged to use scratch paper or Chrome Canvas as a scratch pad. You are allowed to check your calculations with a calculator.

check stub

The amount for SOCIAL SECURITY TAX for this pay period was $

Answers

Answer:

292.32

Step-by-step explanation:

i took 9.75 times 30 and then minus 10% minus 6.2% and minus 1.45% and got that answer

The tallest man in the world is about 101 inches tall. The shortest man in the world is about 29 inches tall. How much taller is the tallest man than the shortest man?

Answers

Answer:The tallest man is 72 inches taller than the shortest man.

Step-by-step explanation:

Subtraction:

101in-29in=72inches

Answer:

72 inches taller

Step-by-step explanation:

29in+x=101x=101-29x=72

Anybody know this need help??

Answers

Answer:

42 mi

Step-by-step explanation:

To find the perimeter, just add up all the side lengths.

13 + 14 + 15 = 42

Note this is mi and not mi² since this is not area.

Answer:

i think i know. . if its asking for the perimeter, its talking about around the triangle soooo C

Step-by-step explanation:

I'm sorry if you get it wrong. .

Guys I need help ASAP I am giving 55 points

Answers

Answer:

The answer is 80°

Step-by-step explanation:

pls give brainliest!

all angles = 360°

100+100+80=280°

360°-280°=80°

February 29th is on Sunday. on what day will the next February 29th be?​

Answers

Answer: Friday

Step-by-step explanation:

If February 29th is on a Sunday, then, the day that the next February 29th will fall on will be Friday.

First and foremost, we should realise that February has 28 days but in leap years which takes place every 4 years, it has 29 days.

We should realise that the dates in the calendar are arranged in such a way that if a particular date falls on a particular day this year, the date will fall on the next day next year. e.g. since January 20 falls on. Wednesday this year, it will fall on a Thursday next year.

Since February 29 is a date for a leap year, following the above explanation, if February 29th is on a Sunday, then, the day that the next February 29th will fall on will be Friday which is in the next four years.

In a juggling competition, 7/ 20 of all the jugglers use balls only, 3/ 7 of all the jugglers use rings only, and the rest of jugglers use both balls and rings. If there are less than 200 jugglers in the competition, how many jugglers use both balls and rings?

Answers

Answer:

44

Step-by-step explanation:

Number who use balls only = 7 / 20

Number who use rings only = 3/7

Fraction who use both :

1 - (7/20 + 3/7)

1 - 0.7785714

= 0.2214285

If number of jugglers is less than 200

Number of jugglers who use both :

0.2214285 * 200

= 44.285714

Number of jugglers who use both should be about 44

????????????????????

Answers

Answer:

180 - y

Step-by-step explanation:

The exterior angle is equal to 180 minus the interior angle.

Answer:

The total angle a triangle have is 180

so now subtract it by 50

180-50 = 130

and the other angle we get is by subtracting 180-92 which is 88

y=88 degree

now x=180-(88+50)

=42

so x=42

Need help asap Pleaseee

Answers

Answer:

the answer is 144 feet and I don't really have an explanation

Answer:

Radius = 12 feet

Step-by-step explanation:

The area of a circle formula is Area = pi r^2 ("r" represents the radius)

The area of Circle Q is 144pi

You can substitute "Area" with 144pi, which would look like this:

144pi = pi x r^2

Now divide both sides with "pi", which gives:

144 = r^2

Finally, square root both sides:

sqrt(144) = sqrt(r^2)                     (sqrt = square root)

And that gives

12 = r

So the radius is 12 feet.

On the youth soccer team 3 out of 12 team members have played in previous years. Based on this information , if 180 kids are in the youth soccer league , then how many could be expected to have played the year before

Answers

Answer:

its 3/12 ×180 which is 1/4 of 180 as similar which is = 45. So we find out that 45 members where involved last year in youth soccer league.

Please help me, 30 points, really easy.

Find the missing dimension. Use the scale factor 1 : 12.

Answers

Answer:

15in

Step-by-step explanation:

Convert the 15 ft to inches (180) and then set up the proportion.\frac{1}{12} = \frac{x}{180}121=180x .  Cross multiply to get that 12x = 180 and x = 15 inches.

I think it’s 15 sorry if I get it wrong

2/3 + 9/12 add fractions with unlike denominators

Answers

Answer:

[tex]1\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3} + \frac{9}{12}[/tex]   <-- let's change 2/3 into a fraction that has 12 as the denominator

[tex]\frac{2}{3}[/tex] × 4   <-- multiply both the numerator and the denominator by 4

2 × 4 = 8   <-- new numerator

3 × 4 = 12   <-- new denominator

now we have [tex]\frac{8}{12}[/tex] + [tex]\frac{9}{12}[/tex]

[tex]\frac{8}{12}[/tex] + [tex]\frac{9}{12}[/tex] = [tex]\frac{17}{12}[/tex]    <-- let's change it into a mixed number

17 ÷ 12 = [tex]1\frac{5}{12}[/tex]

Answer: its 17/12

Step-by-step explanation:

-2(v – 7) – 8v(-2v – 8)

Answers

Answer:

= 16v^2+62v+14

Step-by-step explanation:

I recommend you using the website "Symbolab Algebra Calculator". It will really help you.

Find the area of the shaded region. Round your answer to the nearest hundredth.
6 m
IT T
24 m
The area is about
square meters

Answers

The area of the shaded region in the circle to the nearest hundredth is 1695.60 meter squared.

Area of a circle

area = πr²

where

r = radius of the circle

The area of the shaded portion is the difference of the area of the large and small circle.

Therefore,

area of the large circle = πr²

area of the large circle = 3.14 × 24²

area of the large circle = 3.14 × 576

area of the large circle = 1808.64 m²

Therefore,

area of the small circle = 3.14 × 6²

area of the small circle = 3.14 × 36

area of the small circle = 113.04 m²

The area of the shaded region  = 1808.64 - 113.04 = 1695.6 m²

learn more on area here: https://brainly.com/question/16761235

Triangle JKL is formed by plotting three points, as shown below. What is the length of side
JK?

Answers

Answer:

5

Step-by-step explanation:

You have to add the boxes between j and k and that’s how u get your length

Approximate the solution of the system to the nearest thousandth.

Answers

Answer:

(-0.67412648,-047682599)

Step-by-step explanation:

Jordan made a wooden square box. All sides of the wooden are 6 cm. If he wants to increase the length of all sides by 1.6 cm, what will be the perimeter and area of the new box

Answers

The answer is :
Perimeter : 30.4 cm
Area : 57.76 cm^2
Hope it helped!

Answer:

Perimeter: 30.4 cm

Area:57.76

Step-by-step explanation:

6cm+1.6cm=7.6cm

Perimeter:7.6x4

Area:7.6x7.6

A sandwich store chargers a $10 delivery fee, and $4.50 for each sandwich.

what is the total cost (sandwiches and delivery charge) if an office orders 6 sandwiches.

Formula (y=mx+b)

Answers

Answer:

$37

Step-by-step explanation:

Delivery fee- $10

each sandwich- $4.50

Sandwiches ordered- 6

4.50(6)+10=37

I don’t understand this

Answers

Answer:

3 to 1

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, that is

OA' : OA

= 27 : 9 ( divide both parts by 9 )

= 3 : 1

Alyssa has $75 less than three times Eric. Together they have $905. How much money do they each have?

Answers

Answer:

Alyssa=225

Eric=680

Step-by-step explanation:

The money Alyssa has $660 and  Eric has $245.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Alyssa has $75 less than three times Eric.

Let $x be the money Eric had.

Then Alyssa has 3x-75

Together they have $905.

So, x+3x-75=905

4x=905+75

4x=980

x=980/4

x=$245

Money Alyssa has 3x-75

= 3×245-75

= 735-75

= $660

Therefore, money Alyssa has $660 and  Eric has $245.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

please help! algebra 2

Answers

im sure Its the last one

Help and explain please?

Answers

Square root of 160.

Use Pythagorean’s Theorem.
a^2+b^2=c^2
(12)^2+(4)^2=c^2
144+16=c^2
160=c^2
C=square root of 160

Merry has a pipe that she wants to cut into 4 pieces. If the pipe is 26 2/3 feet long, how long should she cut each piece?

Answers

Answer: 6 2/3 ft

Explanation:

1. Turn the mixed number (26 2/3) into an improper fraction by multiplying 26 by 3 and then adding 2. (26x3=78)(78+2=80=80/3)

2. Now divide 80 by the number of pieces she’s cutting (4). (80÷4=20)

3. Now divide 20 by the denominator (3) to convert it back into a mixed number. (20÷3=6 2/3)

A shipping box has the dimensions shown 1/4 1/4 and 1/2, What is the volume of the box in cubic yards.

First 3 people get a brainly

Answers

Step-by-step explanation:

what is the unit of measurement for the 1/4, 1/4, and 1/2?

A landscaper needs to fill a path measuring 2 feet by 6 feet with patio stones.
The patio stones are ench 1 foot by 2 feet, so the landscaper calculates that she
will need 6 of them,
Before arranging the patio stones, the landscaper wants to look at all of her
options. She cannot cut or overlap the stones, and they all must fit inside the
path area without any gaps. Two possible arrangements of the stones are shown
below. How many different arrangements are there in total?

Answers

Answer:

28

Step-by-step explanation:

You can have 8 1x2 verical in a row,

7 with two horizontals stacked on top of each other.

9 with 4 horizontal tiles,

10 with 6 horizontal tiles,

1 8 horizontal tiles set,

1+7+1+9+10=28

Solve for x*
X+ 19
14 + x

Answers

Answer:

x=-9

Step-by-step explanation:

2(14+x)=x+19

28+2x=x+19

x=-9

direct and inverse variation

Answers

Answer:

4 workers can do the job in 18 days.

Step-by-step explanation:

The number of days d varies inversely as the number of workers.

We can write it as: [tex]d\: \alpha\: \frac{1}{w} \\d=\frac{k}{w}[/tex]

where k is constant of proportionality

We are given: If it takes 9 days for 8 workers to complete the job, then how many workers would it take to do the job in 18 days.

d = 9, w = 8

d = 18, w =?

First we will find value of k when d = 9, w =8

[tex]d=\frac{k}{w}\\9=\frac{k}{8}\\k=9*8\\k=72[/tex]

The value of k, will remain same as it is constant.

We get k = 72.

So, Now we have d = 18, k = 72 and we need to find w

[tex]d=\frac{k}{w}\\18=\frac{72}{w}\\18w=72\\w=\frac{72}{18}\\w=4[/tex]

So, 4 workers can do the job in 18 days.

what does y equal?......​

Answers

Answer:

37

Step-by-step explanation:


4. An angle is 50° more than its supplement. Find the angles.

Answers

Answer:

The angles measure [tex]65[/tex]° and [tex]115[/tex]°.

Step-by-step explanation:

Supplementary angles are a pair of angles whose measures add up to [tex]180[/tex]°. In this case, we know that one angle is [tex]50[/tex]° bigger than the other one, so if we let the measure of one angle be [tex]x[/tex], then the measure of the other angle will be [tex]x+50[/tex]. Therefore, we can write the following equation to solve for

[tex]x+x+50=180[/tex]

Solving for [tex]x[/tex], we get:

[tex]x+x+50=180[/tex]

[tex]2x+50=180[/tex] (Simplify LHS)

[tex]2x+50-50=180-50[/tex] (Subtract [tex]50[/tex] from both sides of the equation to isolate [tex]x[/tex])

[tex]2x=130[/tex] (Simplify)

[tex]\frac{2x}{2}=\frac{130}{2}[/tex] (Divide both sides of the equation by [tex]2[/tex] to get rid of [tex]x[/tex]'s coefficient)

[tex]x=65[/tex]

Therefore, [tex]x+50=65+50=115[/tex], so our final answer is that the angles measure [tex]65[/tex]° and [tex]115[/tex]°. Hope this helps!

What is the volume of this cylinder?
8cm

20cm

Answers

Answer:160

Step-by-step explanation:

Answer:

there is no picture but if you make another post with the picture, I will more than gladly answer it  :)

Step-by-step explanation:

subject: [Mathematics]​

Answers

Answer:

Whole number

rational numbers

natural number

interger

Step-by-step explanation:

Everything but irrational I think
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