-Let g(x) be a function defined by g(x) = x3.
a) Sketch the graph of g(x).
b) Find the inverse g-1(x) of g(x) then sketch the graph of g-1(x). c) Specify the domain and range of g(x) and g-1(x).
d) Determine the end behavior of g(x) and g-1(x).

Answers

Answer 1

Answer:

Step-by-step explanation:

a) The graph rises steeply from the third quadrant  and there is a point of inflection through  the origin (0, 0) then rises steeply in quadrant 1.

b) Let y = g(x) = x^3

x = ∛y

So g(-1)x = ∛x.

The graph is the reflection of g(x) in y = x.

c) Domain of g(x) = All real x, Range is all real g(x).

Domain of  g(-1)x  = All real x, Range = all real g-1(x).

d) You will see the end behaviour from the graphs.

I tried to send you a link to the graphs but the system wont allow it.


Related Questions

Helpppp!!!!!! After a few rides, your friends are ready for some ice cream! You stop into Scoops to You for some ice-cream. Which is the better deal?
3 scoops for $3.69

2 scoops for $2.69

1 scoop for $1.79

Answers

Answer:

3 scoops for $3.69  is better deal.

Step-by-step explanation:

Given that,

There are 3 deals to buy icecram.

3 scoops for $3.69  

2 scoops for $2.69  

1 scoop for $1.79

We can find the cost of 1 scoop for each deal. So,

First deal,

1 scoop = 3.69/3 = $1.23

Second deal,

1 scoop = 2.69/2 = 1.345

We can see that the cost of 1 scoop for deal 1 is less than others. It means first deal is best.

−4x+7y=3 what are the intercepts!!!!!

Answers

I got x= -3/4 and y= 3/7

Can someone help me with this problem and help me understand it better

Answers

Answer:

Proved

Step-by-step explanation:

Given

The attached table

Required

Prove that Lydia is incorrect

Firat, calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where:

[tex](x_1,y_1) = (5,19)[/tex]

[tex](x_2,y_2) = (4,15)[/tex]

So, we have:

[tex]m = \frac{15 - 19}{4 - 5}[/tex]

[tex]m = \frac{-4}{-1}[/tex]

[tex]m=4[/tex]

The equation is then calculated using:

[tex]y - y_1 = m(x-x_1)[/tex]

Where:

[tex](x_1,y_1) = (5,19)[/tex] and [tex]m=4[/tex]

This gives:

[tex]y - 19 = 4(x-5)[/tex]

[tex]y - 19 = 4x-20[/tex]

Make y the subject

[tex]y = 4x-20+19[/tex]

[tex]y = 4x-1[/tex]

The above shows the equation. Hence, the Lydia is correct

what is the answer to solve for n

Answers

Step-by-step explanation:

According to pythagoras theorem the square length of hypotenuse is equal to sum of other two sides

n^2 + 19^2 = 15^2

n^2 + 361 = 225 if we subtract 361 from both sides

n^2 = -136 but the root of square cannot be negative

I believe there's a mistake in this question so you should ask your teacher.

What is the length of the unknown side?
16
12
A 14 units
B) 20 units
C 28 units
D) 200 units

Answers

Answer:

B)20 Units is the answer for it

Which of the I-values are solutions to both of the following inequalities?
81> I and I > 68

Answers

Answer:

Option (C)

Step-by-step explanation:

Given inequalities are,

81 > x and x > 68

Therefore, 81 > x > 68 is the inequality representing the solution area for x.

Out of x = 88, 85 and 80,

x = 80 will lie between the range of x = 68 and x = 81.

Therefore, Option (C) will be the correct option.

Count box lengths to identify the base and height. Then, find the area of the triangle.

How many square units is this triangle?

Answers

Answer:

14 units²

Step-by-step explanation:

1/2(7)(4)=14 units²

Answer:

14 square units

Step-by-step explanation:

¿Cómo se dice 80 en números romanos?​

Answers

Answer:

PLEASE MARK ME BRAINLEST...

Step-by-step explanation:

Para leer y escribir correctamente el número 80 como número romano LXXX, debe leerse y escribirse de izquierda a derecha, y de mayor a menor número.

Answer:

Guessing that Romanos means Roman Numerals = LXXX

Step-by-step explanation:

L=50

X=10

10X3= 30

30+50=80

28% of what number is 7? Round your answer to the nearest tenth.

Answers

Answer:

25

Step-by-step explanation:

hope i helped, if u have any additional questions feel free to reply here or msg me on ig (/craxzyx) !! <3

25 iS THE ANSEWR SO NOW JUST ROUND

True and false
Urgent!!! Please help man!

Answers

Answer:

True

Step-by-step explanation:

Because I did this.

True because I did this

Given the set of ordered pairs, do the following.
a. mapping
b. table
c. graph
1. {(0, 0), (1, -1), (1, 1), (4, -2), (4, 2)}
2. {(10, 0), (10, 2), (10, 4), (10, 6), (10, 8)}

Answers

This is for the table

X | 0, 1, 1, 4, 4
Y | 0,-1,1,-2,2


X | 10,10,10,10,10
Y | 0,2,4,6,8

The area of a rectangle is 2x*2-13x+12 and another area is 6x^2-13x+21, what is the combined area of both rectangles?

Answers

Answer:

8x^2 - 26x + 33

Step-by-step explanation:

Add the expressions.

2x^2 - 13x + 12 + 6x^2 - 13x + 21 =

= 2x^2 + 6x^2 - 13x - 13x + 12 + 21

= 8x^2 - 26x + 33

Write the sentence as an equation.

163 reduced by p is 291

Answers

Answer:

163 - p = 291

Step-by-step explanation:

Answer:

Here are some examples.

f(x) = [tex]x^{4}[/tex] - 6

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

f(x) = 3[tex]\sqrt[]{3}[/tex] + [tex]x^{2}[/tex]

Step-by-step explanation:

Hope I could help. Brainliest??

NEED HELP W GEOMETRY

In △
ABC, ∡A
is 2 more than twice ∡B
, and ∡C
is 7 less than twice ∡B
. What is the measure of each angle in △
ABC and what is its classifications?

Answers

Answers:

Angle A = 76Angle B = 37Angle C = 67

Triangle ABC is an acute triangle. It's also a scalene triangle.

====================================================

Work Shown:

x = measure of angle B

2x+2 = measure of angle A, since we're told its "2 more than twice angle B"

2x-7 = measure of angle C, for similar reasoning

The three angles add to 180. This is true for any triangle

A+B+C = 180

(2x+2)+(x)+(2x-7) = 180

5x-5 = 180

5x = 180+5

5x = 185

x = 185/5

x = 37

This means angle B is 37 degrees. The other two angles are

A = 2x+2 = 2*37+2 = 74+2 = 76

C = 2x-7 = 2*37-7 = 74-7 = 67

----------------

In summary, we have these three interior angles

A = 76B = 37C = 67

As a way to check, note how A+B+C = 76+37+67 = 180. This confirms the answer. All three angles mentioned are smaller than 90 degrees, so this triangle is acute.

Furthermore, because all three angles are different measures, this means all three sides are different lengths. This leads to triangle ABC being scalene.

Helpppop meeeee plzzzzz

Answers

Answer:

7.4

Step-by-step explanation:

solve for side a in first triangle:

[tex]10^2-6^2=y^2[/tex]

100-36=[tex]\sqrt{64}[/tex] (take square root of 64)

y=8

then use 8 to solve for x:

[tex]8^2-3^2=x^2[/tex]

64-9=[tex]\sqrt{55}[/tex] (take square root of 55)

x=7.4

D'Andre earns some money by helping people with their yards. It takes him an average of 2 hours to weed a flowerbed and an average of 1.5 hours to mow and edge a lawn. He can work no more than 6 hours a day. He charges $60 to weed a flowerbed and $75 to mow and edge a lawn. He needs to cover his expenses of $150 to make a profit. Write a system of inequalities that would help determine how many flowerbeds and lawns he could complete on a given day.
______________________________
plz help its due like rn so I'll give brainliest ​

Answers

Answer:

3 flowerbeds and 5 lawns.

Step-by-step explanation:

I promise.

A photograph is in the shape of a rectangle. It has a Iength of (x + 2) inches and a width of (x -2) inches. What is the area of the photograph?

Answers

Answer:

The area of the photograph is:  [tex]A=x^2-4[/tex]      

Step-by-step explanation:

Given

The length of rectangular photograph = [tex]l[/tex] = (x + 2) inches

The width of rectangular photograph = [tex]w[/tex] = (x - 2) inches

To determine

The area of the photograph

Important Tip:

Given that the photograph is in the shape of a rectangle. Thus, we can use the formula involving the area of a rectangle to determine the area of a photograph.

The Area of the photograph can be determined using the formula

[tex]A = wl[/tex]

where

[tex]A[/tex] is the area[tex]l[/tex] is the length[tex]w[/tex] is the width

now substituting [tex]l = (x + 2)[/tex] and [tex]w = (x-2)[/tex] in the formula

[tex]A = wl[/tex]

[tex]A = (x-2) (x+2)[/tex]

Apply Difference of Two Squares Formula:  [tex]\left(a-b\right)\left(a+b\right)=a^2-b^2[/tex]

[tex]A=x^2-2^2[/tex]       ∵ [tex]a=x,\:b=2[/tex]

[tex]A=x^2-4[/tex]        ∵ [tex]2^2=4[/tex]

Therefore, the area of the photograph is:  [tex]A=x^2-4[/tex]      

Sasha ran 2/3 of a 27km race before she stopped to walk. How
many kilometers had she run at that point?

Answers

Answer:

2/3 of 27=18 km

Step-by-step explanation:

find the measure of the angel x​

Answers

Answer:

80°+30°=180°

=110=180

x=70°

answer

Answer:

80 - 30 = 50

Step-by-step explanation:

bcz sum of two interior angle is equal to one exterior angle

What is the area of a rectangle
7 inches long and 3 inches wide?

Answers

Answer:

21

Step-by-step explanation:

you do 7x3

Write the multiplicative identity using 9.

Answers

Answer:

3*3

Step-by-step explanation:

hope it helps you

thank you

Your teacher tells you that the hour hand on
an analog cl o ck will ro t ate 45 while yo u
w rite a math quiz. If the quiz starts at 9:00,
wh at time does it end? Wh at is the angle
b e t ween the starting and ending positions
of the minute hand?

Answers

Ends at 9:45
That is a right angle.

Tanner had $42.80 and spent 20% of his money on a book including tax. If he paid with a $10 bill, how much change did Tanner get back?

A. $7.28
B. $6.24
C. $1.44
D. $17.54

Answers

C.
42.8 x 0.2 = 8.56
10 - 8.56 = 1.44

Use the rule 2 + 3 to find the missing number on the table.
X Y
0 3
3 6
11
7 10
9 12

Answers

Answer:

14

Step-by-step explanation:

11 + 3 = 14

Hope it helps!

Thanks!

I have to turn this in at 5:00 pls help!!!

Answers

It would be 2/5

There’s 12 bass fish and 30 fish overall

Which equals:
12/30

And then if you simplify 12/30 you get 2/5

Sherbrooke, Quebec is 210 miles from Boston, MA. A train leaves Boston at noon and arrives in Sherbrooke at 4:40 PM. On the return trip to Boston, the train travels 50.4 mph. How many times greater (or less) is the train’s speed on the return trip to Boston than on the trip to Sherbrooke?

Answers

9514 1404 393

Answer:

  1.12 times as great

Step-by-step explanation:

The speed from Boston is ...

  (210 mi)/(4 2/3 h) = 45 mi/h

Then the speed to Boston is ...

  50.4/45 = 1.12 . . . times as great

__

The speed on the return trip is 1.12 times as great, or 12% greater than on the trip to Sherbrooke.

9514 1404 393

Answer:

 1.12 times as great

Step-by-step explanation:

The speed from Boston is ...

  (210 mi)/(4 2/3 h) = 45 mi/h

Then the speed to Boston is ...

  50.4/45 = 1.12 . . . times as great

__

The speed on the return trip is 1.12 times as great, or 12% greater than on the trip to Sherbrooke.

The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 27 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.1 years and a sample variance of 36.0 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls.

Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is SM=_________ .The t statistic is _________. Now suppose you have a larger sample size n 81. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same standard deviation as above, but with the larger sample size. The new estimated standard error is __________ .The new t statistic is___________

Answers

Answer:

a) t-statistic  t = 0.9532

b) The standard error  S.E = 1.2

c) The new  t-statistic = 1.95

d)  The new estimated standard error =0.666

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 16

The sample size n=27

The mean of the sample = 17.1

Given that the variance of the sample (S²) = 36.0

The standard deviation of the sample (S) = √36 = 6

Test statistic

  [tex]t = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

 [tex]t = \frac{17.1 -16}{\frac{6}{\sqrt{27} } }[/tex]

t = 0.9532

b)

   The standard error is defined by

  [tex]S.E = \frac{S.D}{\sqrt{n} } = \frac{6}{\sqrt{27} } =1.154[/tex]

Step(ii):-  

c) given that the sample size n = 81

Test statistic

 [tex]t = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

 [tex]t = \frac{17.1 -16}{\frac{6}{\sqrt{81} } }[/tex]

t = 1.65

d)

The new standard error is defined by

  [tex]S.E = \frac{S.D}{\sqrt{n} } = \frac{6}{\sqrt{81} } = 0.66[/tex]

Factor 3n^2 + 5n - 2
PLZ HELP

Answers

Answer:

(3n - 1)(n + 2)

Step-by-step explanation:

calculate the area of a circle with a diameter of 3m?

with Solution =​

Answers

Answer:

Area of circle = pie r²

= 3.14 × 2.25

=7.065

Answer: 7.07cm²

Step-by-step explanation: diameter=3

radius=d/2

          =3/2

          =1.5cm

area=πr²

       =22/7 x 1.5 x 1.5

       =22/7 x 2.25

       =99/2 ÷ 7

       =99/2 x 1/7

       =99/14

     

Helpppppppp me with question 2 Tuesday pleaseeeeee

Answers

Answer:

firstly we solve mixed fraction i. e .

5/2 +b = 47/4

b. = 47/4 - 5/2

b = 27/4

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Answer:

2 - [tex]b = 9\frac{1}{4}[/tex]

Step-by-step explanation:

Convert the mixed numbers into improper fractions.

2 • 2 + 1 = 5

4 • 11 + 3 = 47

[tex]\frac{5}{2} + b = \frac{47}{4}[/tex]

[tex]-\frac{5}{2} +\frac{5}{2} + b = \frac{47}{4} - \frac{5}{2}[/tex]

[tex]b = \frac{37}{4}[/tex]

[tex]b = 9\frac{1}{4}[/tex]

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