2. Let f(x) = 4x + 12 and g(x) = 4x2 – 12.

(a) What is the inverse of function f?

(b) Is f an inverse of g? Show your work algebraically and explain your answer

Answer:​

Answers

Answer 1

Answer:

  (a) f^-1(x) = 1/4x -3

  (b) f is not the inverse of g

Step-by-step explanation:

(a)

The inverse of function f can be found by solving ...

  x = f(y)

  x = 4y +12

  x -12 = 4y

  x/4 -3 = y

The inverse of function f is ...

  f^-1(x) = 1/4x -3

__

(b)

g(x) ≠ f^-1(x), so g^-1(x) ≠ f(x). Function f is not an inverse of g.

_____

Additional comment

Function g is a quadratic, so it doesn't have an inverse function, except on a restricted domain.

Because g is 2nd degree, any inverse relation will involve a 1/2 power (square root). Both f and its inverse are linear functions, so cannot be inverses of g.


Related Questions

I need a step by step explanation please on this please so I can understand it better

Answers

Answer:

  P = 29 units

Step-by-step explanation:

Let h represent the height of the triangle. Then 2h is the length of the base. The area is given by ...

  A = 1/2bh

  36 = 1/2(2h)(h) = h²

  h = √36 = 6

  base = 2h = 12

The base of the isosceles triangle is 12 units, and its height is 6 units.

__

The altitude line makes a right angle with the base, dividing it into two right triangles with sides of length 6. The hypotenuse (s) of each of those is given by the Pythagorean theorem as ...

  s = √(6² +6²) = 6√2

Then the perimeter of the triangle is ...

  P = base +2s = 12 +2(6√2) = 12(1 +√2) ≈ 28.97 ≈ 29

The perimeter of the triangle is about 29 units.

_____

Additional comment

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides.

For an isosceles right triangle, this means the hypotenuse is √2 times the side length. (This is a useful relationship to remember, as it is used a lot in algebra and geometry problems.) The acute angles in such a triangle are 45°.

Height be xBase be 2x

AtQ

[tex]\\ \rm\hookrightarrow \dfrac{1}{2}(2x)(x)=36[/tex]

[tex]\\ \rm\hookrightarrow x^2=36[/tex]

[tex]\\ \rm\hookrightarrow x=6[/tex]

Base=12

Apply Pythagorean theorem

[tex]\\ \rm\hookrightarrow H^2=6^2+6^2=36+36=72\implies H=8.5[/tex]

Perimeter

2(8.5)+12=17+12=29units

{(2,12), (3,8), (4,6)}

constant:

equation:​

Answers

Answer:

y = x² - 9x + 26

hope to help!!

One angle of an isosceles triangle measures 34º. Which other angles could be in that
isosceles triangle?

Answers

Answer:

112º and 73º

Step-by-step explanation:

34º could be base angle

Base angles are equivalent

Vertical angle would be = 180 - 34 - 34

Vertical angle = 112º

34º could be vertical angle

Base angles are equivalent

2x = 180 - 34

Base angle = 73º

Vern has a collection of pennies, nickels, and dimes. The ratio of the number of pennies to the number of nickels is $9:2,$ and the ratio of the number of nickels to the number of dimes is $3:4.$ If the total worth of Vern's collection is $\$10.96,$ then how many coins do they have in total?

Answers

Let  be the number of pennies,  be the number of nickels, and  be the number of dimes that Vern has. The given ratios tell us that  and  Therefore,  so we haveTo turn this into a ratio of integers, we multiply every part of the ratio by  Doing this, we see that Therefore, we can think of Vern's collection as consisting of several groups, each of which contains  pennies,  nickels, and  dimes. Let  be the number of such groups of coins that Vern has. Then Vern has  pennies,  nickels, and  dimes. Since a penny is worth  cent, a nickel is worth  cents, and a dime is worth  cents, the total worth of Vern's coins in cents is  However, we know Vern has  or  cents, so we can write an equation:Simplifying the left-hand side, we get  Dividing both sides by  we get  This tells us that Vern has  groups of  coins, for a total of  coins.

328

noah neck wth noah neck

Answers

Answer:

a meme

Step-by-step explanation:

Answer:

meem

Step-by-step explanation:

meet bc it is crazy and I luv it

If you buy three of the ABC bonds with $10 commission for each, how much will it cost? a. $3142.50 b. $1047.50 c. $3172.50 d. $1077.50

Answers

The computation shows that the cost of each bond is A. $3142.50.

How to solve the cost?

From the complete information given, the price of the bond is given as $2856.80 each.

Therefore, with the commission, the price will be:

= $2856.80 + (10% × $2856.80)

= $2856.80 + $285.68

= $3142.50

In conclusion, the cost of each bond is $3142.50.

Learn more about cost on:

https://brainly.com/question/25109150

Answer:

it's A

Step-by-step explanation:

maybe

Instead of dividing $15.00 by 2 1/2, double both numbers and then find the quotent.

Answers

6 because its 6 dont ask

Help help help math math

Answers

Answer:

V = 500 cm³

Step-by-step explanation:

V = 4/3 πr³

V = (4/3) × 3 × (5 cm)³

V = 4 × 125 cm³

V = 500 cm³

Kelly bought cups for home. Each cup cost $3. He gave
$40 to the cashier and got $13 back in change. How many
cups did she buy?

Answers

Answer:

40-13=27

3*9=27

She bought 9 cups.

Brainliest plz

20 points.
The midpoint of AB is (-9, -10) and the coordinates of point A are (-1, 9) what are the coordinates of point B? ​

Answers

Answer:

  B = (-17, -29)

Step-by-step explanation:

The midpoint (M) of AB is ...

  M = (A +B)/2

Solving for B gives ...

  B = 2M -A = 2(-9, -10) -(-1, 9) = (-18+1, -20 -9)

  B = (-17, -29)

4) The yellow submarine was at sea level when the passengers boarded. The journey began with a descent of 40 meters. After examining the sea life, they rose 30 meters. Zach thought he saw an octopus, below. They dove again, a distance of 25 meters to watch the eight ‘legged’ sea creature.
a) Write an expression to describe the journey of the yellow submarine. _________________________________

b) At what depth did they stop to look at the octopus? ______________________

Answers

a) Write an expression to describe the journey of the yellow submarine.

-> ((0 - 40) + 30) - 25

[] Sea level = 0

[] The descend 40 meters = -40

[] After examining the sea, they rose 30 meters = + 30

[] They dove 25 meters to look at an octopus = -25

b) At what depth did they stop to look at the octopus?

-> -35 meters

[] The started at 0 (0), descended 40 (-40), rose 30 (-10), and then sove 25 (-35) to see the octopus

[] Another way to think of this is to simplify our previous expression completely

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

A local business charges $20 to set up their sweatshirt printing machine with the design and $9.75 in materials per sweatshirt to print.

1. Write an equation for the average cost A(x) of printing x sweatshirts through this company.

2. Describe what happens to the average cost per sweatshirts as more and more are printed.​

Answers

IM SURE ITS DEFINITELY NOT BUT POSSIBLE 19

Which event is important enough to include in a summary of this
story? Add the event to the chart.
D Event
Event
Event
Hester gives Ms.
Walker the letter
explaining her idea.
Ms. Walker agrees
to consider
Hester's idea.
?
Hester repeats a
*) phrase in her mind
over and over.
D
Hester packs up
her things when
the bell rings.
D
Hester returns to
her desk to read
her book.
Hester learns
about another way
to boost her grade.

Answers

When making a summary, it is important to read and understand the text which you are writing.

What is a Summary?

This refers to the concise representation of the main points of a literary text without the use of bias.

Hence,w we can see that because the question is incomplete, you would need a general overview to understand it, so it would be best if you:

Read the given textUnderstand the plot and characterizationFollow the Rising Action, Climax, and Falling ActionList out the main pointsThen, join them in order of occurrence.

Read more about summary here:

https://brainly.com/question/25605883

#SPJ2

what is the answer to 'Which problem would be solved using multiplication, and what is the solution to the problem?'

Answers

Answer:

Jim is 12 years old. Anna is 3 times older than Jim. Calculate Anna’s age using multiplication.

Step-by-step explanation:

The problem above is solved by using multiplication and the solution to the problem is 36.

you multiply 12 * 3 and you get 36.

hope that helps!

PLEASE HELP!! question in picture

Answers

Answer:

you speak English or Espanol? I dont wanna answeri with the wrong language

Use the Binomial Theorem to expand the binomial. SHOW STEPS
(d-4b)^2

Some one please help!!!

Answers

The binomial theorem says

[tex]\displaystyle (a + b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k \\\\(a+b)^n= \binom n0 a^n + \binom n1 a^{n-1}b + \cdots + \binom n{n-1} ab^{n-1} + \binom nn b^n[/tex]

where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient. The binomial coefficients follow a neat pattern called Pascal's triangle:

1

1   1

1   2   1

1   3   3   1

1   4   6   4   1

where the n-th row, starting with n = 0, lists the coefficient of the k-th term in the sum (with 0 ≤ k ≤ n). For example,

[tex]\displaystyle n=0 \implies (a + b)^0 = \sum_{k=0}^0 \binom nk a^{0-k} b^k = \binom00 a^{0-0} b^0 = \underline{1}[/tex]

[tex]\displaystyle n=1 \implies (a + b)^1 = \sum_{k=0}^1 \binom 1k a^{1-k} b^k = \binom10 a^{1-0} b^0 + \binom11 a^{1-1}b^1 = \underline{1}a + \underline{1}b[/tex]

[tex]\displaystyle n=2 \implies (a + b)^2 = \sum_{k=0}^2 \binom 2k a^{2-k} b^k = \binom20a^{2-0}b^0+\binom21a^{2-1}b^1+\binom22a^{2-2}b^2 = \underline{1}a^2 + \underline{2}ab+\underline{1}b^2[/tex]

Each row starts and ends with 1, and every coefficient in between is obtained by adding the coefficients directly above and to the left. The next row, for instance, would be

1   1 + 4   4 + 6   6 + 4   4 + 1   1

or

1   5   10   10   5   1

which is to say,

[tex]\displaystyle (a + b)^5 = \underline{1}a^5+\underline{5}a^4b+\underline{10}a^3b^2+\underline{10}a^2b^3+\underline{5}ab^4+\underline{1}b^5[/tex]

In your case, we have (d - 4b)², so we take a, b, and n above with d, -4b, and 2, respectively:

[tex]\displaystyle (d - 4b)^2 = \sum_{k=0}^2 \binom 2k d^{2-k} (-4b)^k[/tex]

[tex]\displaystyle (d - 4b)^2 = \sum_{k=0}^2 \binom 2k (-4)^k d^{2-k} b^k[/tex]

[tex]\displaystyle (d - 4b)^2 = \binom20 (-4)^0 d^{2-0} b^0 + \binom21 (-4)^1 d^{2-1} b^1 + \binom22 (-4)^2 d^{2-2} b^2[/tex]

[tex]\displaystyle (d - 4b)^2 = 1\cdot1\cdot d^2\cdot1 + 2 \cdot (-4) d \cdot b + 1 \cdot 16 \cdot 1 \cdot b^2[/tex]

[tex]\boxed{(d - 4b)^2 = d^2 - 8bd + 16b^2}[/tex]

Help ~ with this question~

[tex]4 + 4 \div 5[/tex]

Answers

I just added 4 plus 4 to get 8 then divide by 5 which become the decimal 4.8……

Answer:

4.8

Step-by-step explanation:

[tex]\sf 4+4\div 5[/tex]

[tex]\sf 4\div 5 =0.8[/tex]

[tex]\sf 4+0.8[/tex]

[tex]\sf 4.8[/tex]

* Hope it helps, ty 4 pts!

* Have a good day!

Matthew is shrinking
a photograph picture
with an area of 8
square inches on the
computer. He plans
to reduce the area by
25%. What will be the
area in square inches
of the reduced
photograph?

Answers

The area of the reduced photograph is 7.45

Find the value of x so that the ratios are equivalent.

9:x and 54:8

Answers

Answer:

1 and 1/3.

Step-by-step explanation:

Just ask!

Hope this helps...(sorry if I'm wrong.)

(✿◡‿◡) HAPPY HOLIDAYS!!!

720 inches per second to miles per minute

Answers

Answer:

0.681818 miles per min

Step-by-step explanation:

1. 81 1/2 x 27 1/3

2. 32x = 729



Answers

Answer:

1.

Step-by-step explanation:

1. 1.811/2=3.622 271/3=813

3.622*813=2,944.686

this is number one

2. 32x=729

divide both sides by 32

32x=729/32=

22.78125 approximate=22.8 or 23

Can someone help me with this, and if you can Explain it.​

Answers

Answer:

20

Step-by-step explanation:

Since C is the midpoint of BD, BC must be equal to CD. Therefore, we can set the equation:

x+4=3x-10

Solve:

14=2x

x=7

Then we find AC, which is:

2x-5+x+4 = 3x-1

We can plug x in to get:

3*(7)-1=20

rachel got prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 22 cents per yard. If after that purchase there was $19.88 left on the car, how many yards of ribbon did rachel buy.

Answers

Answer:

46 yards.

Step-by-step explanation:

Subtract the new balance from the original balance:

30.00 - 19.88 = 10.12

Therefore, Rachel spent $10.12

Divide the result by the cost of ribbons per yard:

10.12 ÷ 0.22 = 46

Therefore, Racheal bought 46 yeards of ribbon.

The length of a rectangle is equal to three times the width.Find the dimensions of the rectangle if the perimeter is 86 centimeters.

Answers

Answer:

length: 32.25 cmwidth: 10.75 cm

Step-by-step explanation:

Let w represent the width. Then 3w represents the length. The perimeter formula is ...

  P = 2(L +W)

  P = 2(3w +w)

  86 cm = 8w

  w = 10.75 cm

  3w = 32.25 cm

The rectangle is 32.25 cm long and 10.75 cm wide.

Isaiah is saving 12$ per week from his allowance. after 20 weeks, Isaiah has 240$

Answers

Answer: He saved $12 per week

Step-by-step explanation:

I am confused you basically solved your own question but here is the explanation.

Isaiah gets $12 per week in his allowance, every two weeks he gets $24, so in twenty weeks he would have save $240. Here is an equation.

2W*10 = $240

W = weeks

2 weeks = $24*10 = $240

I hope this helps in anyway

Plzzzzz help plzzzzz help meeee

Answers

The answer would be D. Seven hundred thousand nine hundred and four

simplify the expressions 4y+2x-y+8​

Answers

Hey there!

4y + 2x - y + 8

= 4y + 2x - 1y + 8

COMBINE the LIKE TERMS

= (4y - 1y + (2x) + (8)

= (4y - y) + (2x) + (8)

= (2x) + (4y - y) + 8

= 2x + 3y + 8

Therefore, your answer is: 2x + 3y + 8

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

3y+2x+8

Step-by-step explanation:

All you really do is combine the like terms, which in this case is the 3y and the -y. think of the y more as -1y and that is why it's subtrcated.

Help me please I do not want a bot answering with a link

Answers

[tex]\text{Given that,}\\\\\text{First term,}~ a_1= -\dfrac 16\\\\\text{Common ratio,}~ r = 2 \\\\\text{nth term}~ a_n = a_1 r^{n -1} = -\dfrac 16 \left(2^{n-1}\right)[/tex]

Which of the following equations could be the result of using the comparison method to solve the system shown?



x + 2y = 6

x - 4y = 8

2y - 6 = 4y + 8
6 - 2y = -4y + 8
6 - 2y = 4y + 8

Answers

Answer:

                            6 -2y =4y + 8

Answer: 6 -2y =4y + 8

Step-by-step explanation:

compare. 2 1/4 and 3 /14

Answers

Answer:

[tex]\frac{1}{4}[/tex] is larger than [tex]\frac{3}{14}[/tex]

[tex]\frac{1*14}{4*14}[/tex] = [tex]\frac{14}{56}[/tex]

[tex]\frac{3*4}{14*4}[/tex] = [tex]\frac{12}{56}[/tex]

i cant tell if it is [tex]\frac{1}{4}[/tex] or 2 [tex]\frac{1}{4}[/tex]

but if it is 2 [tex]\frac{1}{4}[/tex] that mean this is a mixed number

and [tex]\frac{3}{14}[/tex] is a proper fraction

Other Questions
I need help with 9 and 10 What is the value of 40 1/23 1/2 Which resource would contain the LEAST useful information forresearch concerning air pollution?Bank fornomicelopment incaA)An environmentalist study on emissions controlB)An editorial questioning the effectiveness ofrecyclingA government website about pollution and wastemanagementncy for thench-Eakingmmunity (seeernationalganization ofFrench-D)A doctoral dissertation about air pollution as a causefor global warmingesling astronauts appear weightless while working in the international space station because Solve the inequalities d/13_>-3 The top row contains solutions for the value of c. The bottom row contains equations that must be solved to find c. Drag each solution into the box with the matching equation.720129c is 4 times as many as 5.27 is c times as many as 3.6 times as many as c is 72.8 more than c is 15. which one is it?? I think the answer is B or D but I dont know which one to choose because I feel like they both could be right.What is the universal theme of this passage?Jos and Amador were best friends and did everything together intheir small town of Cosal, Mexico. After taking an art class together,both boys became interested in painting. They'd spend long hours inthe shed on Amador's farm, painting and looking at art books. Theydreamed of attending the School of Fine Arts in San Miguel de Allendeupon graduation. They made a pact that one wouldn't leave the other,and, as luck would have it, both boys gained admission to the school.But the summer before they were to begin art school, Amador's fatherbadly hurt his back, and Amador knew he had to stay and take over thefarm. Amador told Jos to go on without him; Jos agonized over hisdecision, but he went. In San Miguel de Allende, Jose's work suffered.He couldn't translate the emotions he was feeling onto the canvas, sohe either ended up with half-finished work or he simply didn't paint atall. Instead, he stayed up all night looking at the farm pictures Amadorposted on social media sites, wondering if his best friend still painted. He wanted to call Amador so badly, but he just couldn't bring himselfto do itA. Guilt can sometimes be an obstacle to achieving success.B. Friends will always be important no matter how far away they are.C. Sometimes you have to lose everything to learn what's reallyimportantD. Letting go of the past is an important part of growing up. The rocket club is 60% boys. The number of boys is 3 less than 2 times the number of girls. Hovmany girls and how many boys are in the club? [tex]3^{2x+1} -4.9^{x} =-9[/tex] Alguien me dice que debo hacer aqui porfavor es para un examen Which is the equation of a parabola with Vertex (0,0) and directrix x=-2? 44,880 2 poir 8) A pen cost $39 and a pencil cost $17 less. What is the total cost of one pen and two pencils? * Why are Flowers considered as the reproductive part of a plant what happens in the big bang theory How are regional intergovernmental organizations (IGOs) different fromorganizations like the United Nations?A. They are able to pass laws that must be obeyed in all memberstates.B. They are more likely to use military force to achieve members'objectives.C. They are more restrictive about which countries may becomemembers.D. They are completely independent from member states' politicalleaders. Please help. Will give brainliest. Part AAs an object moves around, on which quantities does the change in its gravitational potential energy depend? Choose all thatapply. Is 111111 divisible by 37? Help needed read carefullyI got a 30 on a math test and t hmm e only way to get 65 (passing grade) is to solve the mystery numberI am a factor of 5 and when you pair me up with 15 I am almost a gcm of 30I am larger than 20 and less than 40what number am i? Force = 30 N. Mass = 5 kg. Calculate Acceleration