Consider the function g(x) shown below over a domain of [1,∞).

g(x) = 2(x – 1)2 – 3

Part A
Determine g–1(x).


Part B
Identify the domain and range of g(x) and g–1(x). Represent the domains and ranges in inequality, interval, and set notation. Describe the relationship between the domains and ranges of g(x) and g–1(x).


Part C
Graph g(x) and g–1(x). Describe the relationship between the graphs of g(x) and g–1(x).

Answers

Answer 1

The inverse of a function may or may not be a function

The function g(x) is given as:

[tex]g(x) = 2(x - 1)^2 - 3[/tex]

(a) Inverse function g^-1(x)

We have:

[tex]g(x) = 2(x - 1)^2 - 3[/tex]

Replace g(x) with y

[tex]y = 2(x - 1)^2 - 3[/tex]

Swap the positions of x and y

[tex]x = 2(y - 1)^2 - 3[/tex]

Add 3 to both sides

[tex]x + 3 = 2(y - 1)^2[/tex]

Divide both sides by 2

[tex]\frac{x + 3}2 = (y - 1)^2[/tex]

Take square roots of both sides

[tex]\sqrt{\frac{x + 3}2} = y - 1[/tex]

Add 1 to both sides

[tex]1 + \sqrt{\frac{x + 3}2} = y[/tex]

Rewrite as:

[tex]y = 1 + \sqrt{\frac{x + 3}2}[/tex]

Express as inverse function of g

[tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]

Hence, the inverse function of g is [tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]

(b) The domain, and the range of g(x) and g^-1(x)

Function g(x)

The function g(x) is a quadratic function.

So, the domain is:

Inequality: [tex]-\infty < x < \infty[/tex]Interval: [tex](-\infty ,\infty)[/tex]Set: {R}

The range is:

Inequality: [tex]f(x) \ge -3[/tex]Interval: [tex][-3 ,\infty)[/tex]Set: [tex]\{y|y\ge -3\}[/tex]

Function g^-1(x)

The function g^-1(x) is a square root function.

So, the domain is:

Inequality: [tex]x \ge -3[/tex]Interval: [tex][-3 ,\infty)[/tex]Set: [tex]\{x|x\ge -3\}[/tex]

The range is:

Inequality: [tex]-\infty < y < \infty[/tex]Interval: [tex](-\infty ,\infty)[/tex]Set: {R}

The domain of g(x) is the range of g^-1(x), while the range of g(x) is the domain of g^-1(x).

(c) The graph

See attachment for the graph

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Consider The Function G(x) Shown Below Over A Domain Of [1,).g(x) = 2(x 1)2 3Part ADetermine G1(x).Part

Related Questions

PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS

Answers

Answer:

y = 3x

Step-by-step explanation:

Let's select two points from the given graph.

(1,3) (3,9)

Now, let's use slope formula to find the slope.

m = y2-y1/x2-x1

= 9-3/3-1

= 6/2

= 3

Let's substitute/plug this value into the slope-intercept form.

y = 3x + b

We can see that the y-intercept is 0, from the graph.

b = 0

Therefore,

y = 3x

The volleyball team is having a carwash fundraiser. The cost of each car wash is $5. They sold some season ticket packages, which brought in $1640. The goal of the team is to make at least $2000 from the combined totals of the two fund-raisers. How many cars must they wash in order to meet the team goal of $2000?

Answers

Answer:

They need to wash 72 cars

Step-by-step explanation:

2000 - 1640 = 360

360/5 = 72

Write a compound inequality that the graph could represent.

Answers

Answer:

k < -4 or k > 13

Step-by-step explanation:

Let's take a look at the graph, we can see that the arrows point towards both directions, both dots are open, meaning that we can only have < and > signs. We can see that the arrow pointing to the left contains numbers that are less than -4, so that part of the compound inequality must be k < -4. And on the other side, they are numbers that are greater than 13, so that part must be k > 13. Thus, the answer must be d.

Hopes this helps.

what is 100,100,100,987 times 72

Answers

Answer: 7207207271064

The answer is 7.2072073e+12

10. Sarah wants to buy shirts for her school's
graduation party. A company will make the
shirts for $10.50 each plus a $50 setup
charge. If Sarah has $1000, which inequality
could she use to find the maximum number
of x shirts she can buy?

Answers

Answer:

1000 ≥ 10.50x + 50

Step-by-step explanation:

≥ is a greater than or equal to sign. We want to know how many she could possibly buy.

Find the length of the second base of a trapezoid with one base measuring 18 feet, a height of 5.3 feet, and an area of 125.4 square feet.​

Answers

Answer:

29.32 feet

Step-by-step explanation:

area of a trapezoid = height/2 * (first base + second base)

125.4 = 5.3 / 2 * (18 + second base)

125.4 = 2.65 * (18 + second base)

We want to solve for the second base. To do this, we can start by isolating the (18+second base) by dividing each side by 2.65

47.32 = 18 + second base

subtract 18 from both sides to solve for the second base

29.32 = second base

What is the end behavior of the function shown in the graph above?
A
As x approaches 0, y approaches 15.
As x approaches 25, y approaches 0.

B
As x approaches∞, y approaches 0.
As x approaches −∞, y approaches ∞.

C
As x approaches 0, y approaches ∞.
As x approaches ∞, y approaches −∞.

D
As x approaches ∞, y approaches 0.
As x approaches ∞, y approaches ∞.

Answers

Answer:

B

Step-by-step explanation:

if 4.5 pounds of cherries cost $10 , what is the unit price per pound ? A.$0.22 B.$0.45 C. $2.22

Answers

Answer:

C

Step-by-step explanation:

Divide the price by the weight 10 / 4.5 = $2.22 per pound

hi pls help me solve this​

Answers

Answer:

-23.33

Step-by-step explanation:

C = 5/9 (F - 32)

C = 5/9 (-10 - 32)

C = 5/9 (-42)

C = -23.33

Alex is feeling stressed this morning. He did not get enough sleep because a dog barked most of the night. The dog barked from 11;41p.m. until 12:09 a.m.Then it started barking again at 3:35 a.m. and didn’t stop until 4:10 a.m.How long did the dog bark in all?

Answers

Answer:

Poor Alex, I know how they feel, I got a dog myself.

The amount of time between

11:41 pm to 12:09 am is

19 minutes (to 12 am, 60 minutes to next hour) + 9

which is 28 minutes for the first dog barking session

the second time is 35 minutes,

using same method as before.

adding the two separte barking sessions we get

35+28= 63 minutes

which is equivelant to 1 hour and 3 minutes.

In conclusion the dog barks for 1 hour and 3 minutes in total.

In the partially shown sequence: …, 17711, A, B, 75025, …, each new term is the sum of the two previous terms. Find the whole number value of A. I GIVE BRAINLIEST!

Answers

Answer:

24513

Step-by-step explanation:

help ASAP please hmmmm ​

Answers

Answer:

D. The Number 0.55 Is A Rational Number Because It Can Be Written As The Fraction 11/20.

Step-by-step explanation:

PLEASE HELP!! 100 points!!!


The angle of depression from the top of a tower to a boulder on the ground is 22 . If
the tower is 70 feet high, how far from the base of the tower is the boulder? (Round
answer to the 1st decimal place.)

Answers

Answer:

173.3 feet

Step-by-step explanation:

Let the required distance be x.

We have a right triangle with vertical leg of 70 feet and the acute angle opposite to this leg is 22 degrees.

Use trigonometry:

adjacent / opposite = cotangentx / 70 = cot 22 degx = 70 cot 22 degx = 173.3 feet (rounded)

help please, put how you found it out if you can too !

Answers

Answer:

104 degrees

Step-by-step explanation:

180-(180-(180-(25+85)+65)+31)

Graph the solution to this system of linear inequalities, and describe the meaning of the intersection of all 3 inequalities. HELP ASAP PLEASE!!!​

Answers

Answer:

Step-by-step explanation:

Coordinates ( x, y ) from "red area" satisfy all three inequality.

you travel 90 miles in 1.5 hours. find the speed you travel.​

Answers

Answer:

60 mph

Step-by-step explanation:

Three coffee and two muffins cost a total of 7 dollars. Two coffees and four muffins coast a total of 8 dollars. What is the individual price for a single coffee and a single muffin?

Answers

Step-by-step explanation:

Given,

3 coffee + 2 muffins = $7

and

2 coffees + 4 muffins = $8

let the coffee be x and muffins be y.

so now, we got

3x + 2y = $7 -----------(eqⁿ 1)

2x + 4y = $8 -------------(eqⁿ 2)

multiply (eqⁿ 1) by 2

we got,

2(3x + 2y = $7) = 6x + 4y = $14 -----(eqⁿ 3)

now, subtract (eqⁿ 2) from (eqⁿ 3)

we got,

(6x - 4y = $14) - (2x + 4y = $8)

we got,

4x = $6

x = 6/4 = $1.5

to get value of y put the value of x in eqⁿ2

we got,

2(1.5) + 4y = $8

3 + 4y = 8

4y = 8 - 3 = 5

y = 5/4 = $1.25

hence,

value of one coffee = $1.5

value of one muffin = $1.25

Hope this answer helps you dear! take care!.

please please help!! it’s geometry and im struggling really badly

Answers

Answer:

10. SAS

11. SAS

12. SAS

13. SSS

14. SSS

15.ASA

Step-by-step explanation:

13: SSS 14 : SSS 15:ASA

During crawfish season, Xavier sells crawfish for $62. 50 per sack and charges a $20. 00 delivery fee. Write an equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer.

Answers

The equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer is y = 20 + 62.50x

Given:

cost per sack of crayfish = $62. 50

Delivery fee = $20. 00

y = Total cost

x = sacks of crawfish

The equation:

Total cost = Delivery fee + cost per sack of crayfish(sacks of crawfish)

y = 20 + 62.50x

Therefore, the equation that could be used to determine y, the total cost of x sacks of crawfish delivered to a customer is y = 20 + 62.50x

Learn more about equation:

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The 250 gallons of maple sap will be
boiled until only 3% of its original
volume is left. How many gallons are
left?

Answers

Answer:

7.5 gallons

Step-by-step explanation:

3 x 250/100

= 7.5

Which system of equations is equivalent to the following system? (5 points) 2x + 4y = 14 4x + y = 20

a.2x + 4y = 14
−16x − 4y = −80

b.2x + 4y = 14
−4x + y = −20

c.4x + 8y = −28
4x + y = 20

d.−2x − 4y = 14
4x + y = 20

Answers

Answer:

a.

Step-by-step explanation:

4x+y=20 multiplied by (-4) gives you -16x-4y=-80

Which of the following ordered pairs is the solution to the following system of equations?
X + y = 11
x - 4y = -14
(5,6)
(5-6)
(6,5)
(6,-5)

Answers

(6,5)
To cancel a term from both equations you have to multiple the top one by 4 so
4x + 4y = 44
x - 4y = -14
cancel out the y’s from both equations and add the terms from both so you’ll have
5x = 30
divide by 5
x = 6

substitute 6 for x in the first equation
6+y=11
subtract 6 from both sides
y = 5

A project will take 720 person-days to complete. How many days will it take to complete the project if 5 people work on it?

Answers

720/5= 144, it will take 144 days for 5 people to finish the project.

Solve for x
1. x + 4x = 90

Answers

Answer:

First, you combine like terms.

Then, you divide both sides of the equation by the same term.

Next, you simplify.

Lastly, you have your solution, which is x= 18

Step-by-step explanation:

Hope this helps!

Find the slope of the line passing through the points (-8, -3) and (-3,4).

Answers

Answer:

7/5

Step-by-step explanation:

4 + 3 = 7

-3 + 8 = 5

7/5

Factorize (x-y)^2+(x-y)​

Answers

..............answer..

GRAPHING LINEAR EQUATIONS PLEASE HELP

y=2/5x -3

how do i graph this? i don't know where to start please help!

Answers

Step-by-step explanation:

you can let

x = 0 => y = -3, point ( 0,-3)y = 0 => x = -15/2 = -7.5, point (-7.5,0)

then connect this 2 points

Plz, Help Me!!!
Which graph represents the equation (x + 4)^2 + (y + 5)^2 = 36?

Answers

Answer:

d

Step-by-step explanation:

the center of the circle is at (-4. -5) with a radius of 6

In two or three sentences, summarize what the essay suggests could help women succeed in

business. How does the summary help you identify Sandberg's message, audience, and

purpose?

Answers

The essay suggests women first need to end with internal barriers to succeed in business and this will later destroy external barriers. This helps identify the author's main message, audience, and purpose because it shows the main idea of the essay.

Lean In is an essay by Sheryl Sandberg about gender inequality and the way this inequality has prevented women from being successful and represented in specific areas including government and business.

About business, Sandberg suggests women are quite limited if compared to men due to sexism, sexual harassment, and even internal barriers women create. To stop this situation the author proposes women need to destroy internal barriers such as:

Believing they should do most of the housework and childcare-Believing they cannot be as successful as other women.Holding themselves due to unequal conditions.

Moreover, this idea helps identify other elements of the text by stating the main purpose.

Main message: Women need to destroy mental and internal barriers.Audience: Women.Purpose: To inspire women to end inequality.

Note: This question is incomplete because the text it refers to it is not given; here is the information about the text.

"Lean In: Women, work, and the will to lead" by Sheryl Sandberg.

Learn more about sexism in: https://brainly.com/question/6022376

Translate math sentence in solution.
1.Nine more than a number.
2.One half multiplied by a number.
3.Three more than half of a number.
4. A number increased by seven.
5.Quotient of a number and two tenths.
6.Product of four and a number.
7.Two cubed divided by a number.
8.Difference of ten and a number.
9.Five squared minus a number.
10.Twenty-nine decreased by a number.

Answers

Answer:

[tex]x + 9[/tex]

[tex] \frac{1}{2} \times x[/tex]

[tex]0.5x + 3[/tex]

[tex]x + 7[/tex]

[tex]0.2x[/tex]

[tex]4x[/tex]

[tex] {2}^{3} \div x[/tex]

[tex]10 - x[/tex]

[tex] {5}^{2} - x[/tex]

[tex]29 - x[/tex]

1) n+9
2) 1/2n
3) 1/2n+3
4) n+7
5) n/2/10
6) 4n
7) 2^2/n
8) 10-n
9) 5^2-n
10) 29-n
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