Please answer quickly

Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.

f(x)=x+a/b

g(x)=cx-d


Part 2. Show your work to prove that the inverse of f(x) is g(x).

Part 3. Show your work to evaluate g(f(x)). Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y=x on the same graph.

Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y=x on the same graph.

Task 2

Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation

a√x+b+c=d

Part 2. Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation. Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.

Part 3. Explain why the first equation has an extraneous solution and the second does not.

Answers

Answer 1

f(x)=(x+a)/b

or bf(x)=x+a

let f(x)=y

by=x+a

flip x and y

bx=y+a

or y=bx-a

or f^{-1}(x)=bx-a

also g(x) is inverse of f(x)

bx-a=cx-d

so b=c,a=d

again let g(x)=y

y=cx-d

flip x and y

x=cy-d

cy=x+d

y=(x+d)/c

or g^{-1}(x)=(x+d)/c

also f(x) is inverse of g(x)

so (x+a)/b=(x+d)/c

so a=d,b=c

so in either case a=d,b=c

take b=c=1

a=d=2

f(x)=(x+2)/1=x+2

g(x)=1x-2=x-2

so f(x) and g(x) are two parallel lines f(x) with y- intercept=1 and slope 0

g(x) with y-intercept -2 and slope 0

if we take b=c=2,a=d=3

f(x)=(x+3)/2=x/2+3/2

g(x)=2x-3

here f(x) is of slope 1/2 and y-intercept 3/2

g(x) is of slope 2 and y intercept -3

part 3.

f(f(x))=g((x+a)/b)=c[(x+a)/b]-d=(c/b)(x+a)-d

Answer 2

An inverse function or an anti function exists described as a function, which can change into another function. In other words, if any function “f” carries x to y then, the inverse of “f” will carry y to x.

Part 1: f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2: g(x) = 3x - 2, the inverse.

Part 3: g(f(x)) = x showing that f(x) and g(x) are mutual inverses.

What is inverse function?

An inverse function in mathematics exists function which "reverses" the another function.

TASK 1

Part 1

Let y = f(x) = (x + a) / b

x = g(y) = by-a = cy-d,

so c = b and d = a.

Let d = a = 2 and c = b = 3

f(x) = (x+2) / 3 and g(x) = 3y-2.

Part 2

y = f(x) = (x+2) / 3

3y = x+2  

x = 3y-2 = g(y)

so g(x) = 3x - 2, the inverse.

Part 3

g(f(x)) = 3

f(x)-2 = 3(x+2)/3-2 = x+2-2 = x,

so g(f(x)) = x showing that f(x) and g(x) exists mutual inverses.

x       -2  -1        0    1     2

f(x)    0    1/3   2/3   1    4/3

g(x)  -8   -5      -2    1      4

Part 4

The graph is given below.

TASK 2

Part 1

(a) Let a=1, b=2, c=3, d=6: [tex]$\sqrt{x}[/tex]+2+3=6 ; [tex]\sqrt{x}[/tex]-6=-5

(b) Let a=-1, b=2, c=3, d=4

(a) Multiply both sides by

[tex]$\sqrt{x}+6: x-36=-5(\sqrt{x}+6)=-5 \sqrt{x}-30[/tex]

[tex]$ x-36+30=-5 \sqrt{x }[/tex]

[tex]$ x-6=-5 \sqrt{x}$[/tex]

Square both sides:

[tex]$x^{2} -12 x+36=25 x ; x^{2} -37 x+36=0=(x-36)(x-1)$[/tex].

Part 2

(a) So x=36 or 1 (apparently).

Substitute x=36 in the original equation: 6+2+3=6, 11=6 is not true.

So x=36 is an extraneous solution.

substitute x=1: 1+2+3=6 is true, so x=1 exists the actual solution.

(b) [tex]$-\sqrt{x}+2+3=4 ;-\sqrt{x}=-1$[/tex]; multiply both sides by -1: [tex]$\sqrt{x}=1$[/tex]; square both sides: x=1.

Substitute x=1 in the original equation: -1+2+3=4 is true.

So x = 1 is the solution.

Part 3

(a) the act of squaring both sides resulted in creating an extraneous solution [tex]$\left((-5)^{2} =25=5^{2} \right)$[/tex].  

(b) the solution was simpler and there was no ambiguity.

To learn more about inverse function

https://brainly.com/question/11735394

#SPJ2

Please Answer QuicklyPart 1. Using The Two Functions Listed Below, Insert Numbers In Place Of The Letters

Related Questions

RE
Which graph represents the function f(x) = -X2 + 5?
N
10-
8-
6
2
o
-10 -56-4
ca
M
4
6
8
10
X
do ou

Answers

Answer:

I can't interpret the data the way it is presented.  Are there two columns?  I'll assume "-x2" is really "-x^2."

I've attached a plot of the function.  Check to see which of your points fall on the line.

Step-by-step explanation:

y = -x^2 + 5

The police are searching for a bank that has been on the run for two hours. Based on his running speed, the police believe he could be anywhere within an 8.5 mile radius of the bank. Find the area and circumference of the region in which they must search for the suspect. Round to the nearest whole unit.

Answers

Answer:

π is equivalent to 3.14

Circumfrance =  53

area = 227

Step-by-step explanation:

π is equal to 3.14

Circumfrance = 8.5*2*π

So 8.5 * 2 is 17 times π is 53.38

round to nearest whole number is 53

area is π * radius squared so

8.5 * 8.5 =72.25

* π is 226.865

round to the nearest whole number is 227

PLEASE HELP IT’S DUE TMR!!

Answers

Answer:

see below

Step-by-step explanation:

just reduce to 3 digits before the decimal place and count how many are behind the decimal for what power the 10 is, not including numbers that were already behind the decimal

a. 107.92*10^2

b. 376.932*10^0

c. 998.461*10^3

Answer:

When rounding significant figures the standard rules of rounding numbers apply, except that non-significant digits to the left of the decimal are replaced with zeros.

Step-by-step explanation:

(a) 10792 ≈ 10800

(b) 376.932 ≈ 377

(c) 998461 ≈ 998000

Steel is a mixture of iron, carbon, and other elements. The table shows the number of parts each element in two different-sized samples of steel.

A table with the composition of two samples is shown. Sample one is ninety parts iron, three parts carbon, and seven parts other elements. Sample two is forty-five parts iron, one and a half parts carbon, and three and a half parts other elements.

Question 1
Part A

What is the unit rate of parts iron to parts carbon?

Enter the correct answer in the box.

parts iron per part carbo

Answers

Answer:

Step-by-step explanation:

Sample One, Parts and %      Sample Two, Parts and %

 Fe    90          (90%)                           45             (90%)

   C      3           (3%)                               1.5              (3%)

Other   7            (7%)                            3.5             (7%)

          100 parts                           50 parts

Parts Fe/Parts Carbon = 90/3 or 30/1  in both cases [45/1.5 = 30/1]

What’s the answer to 2(x+3)

Answers

Hello there!

This isn't an equation, but here are some options for what you may be looking for!

Product, Multiplying, Evaluating, and Simplified Form: 2x + 6

Factor: 2(x+3)

Hope I helped,

Brainliest is always appreciated.

Happy Holidays.



4.) Mr. Lakey is a taxi cab driver. He earns $5.00 hour plus tips. One week he works 40
hours, receiving $287 in tips. Find his weekly gross income.

Answers

Answer:

120$

Step-by-step explanation:

What are the solutions to the equation |X – 3|= 14?
x= 11 only
Ox= -11 and x = 17
x= 17 only
x= -11 and x=11

Answers

Answer:

{-11,17}

Step-by-step explanation:

|X – 3|= 14

There are  two solutions to an absolute value, one positive and one negative

x-3 = 14    and x-3 = -14

Add 3 to all sides

x-3+3 =14+3         x-3+3 = -14+3

x = 17                     x = -11

x = {-11,17}

Audrey & Jack begin a candlelight

dinner at 5pm with a 9-inch candle. At

8pm, their candle is only 3 inches.

What is the average rate of change of

the height of the candle per hour?

Answers

Answer:

-2 inches per hour

Step-by-step explanation:

Finding the average rate of change is just like finding the slope. So, take the y values (height) and subtract them and divide that by the difference in the x values (time).

( 3 - 9 ) / ( 8 - 5 )

= -6 / 3

= -2 inches per hour

2√8 -3√50+√32 AHIHIHI

Answers

Answer:

-9.89949493661

Step-by-step explanation:

7. A diver dove to a location 4
a
meters below sea
level. He then dove to a second location meters
below sea level. How many meters are there
between the two locations?

Plz help me quick

Answers

Answer 1 3/5 meter below sea level

In this case, a diver goes into two different location expressed with "meters below sea level" unit. To know the distance between the two location, then you need to subtract it.

Step-by-step explanation:

Distance = 2nd location - 1st location

Distance = 8 1/5 meter below sea level - 6 3/5 meter below sea level= 1 3/5 meter below sea level

help with these questions pls​

Answers

Answer:

1. 5 + r/14

2. 3x -4 = 23

Answer:

1. 5 + r/14

1. 3x - 4 = 23

Step-by-step explanation:

1. Remember, the quotient is obtained by dividing one quantity by another. In the sentence it is stated that "the quotient of r and 14" which means: r divided by 14.

The sentence models 5 + r/14

2. We are to subtract 4 from the product of 3 and x. So part of the equation looks like: "3x-4". Since it is stated that 23 is the total sum, then the answer is: 3x - 4 = 23

There are 75 new houses being built in a neighborhood. Last month, 2/5 of them were sold. This month,1/3 of the remaining houses were sold. How many houses are left to be sold? ​

Answers

You start with 75 houses

2/5 were sold, which mean 3/5 remain
3/5 of 75 is 45

Then, 1/3 of the REMAINING (45) houses were sold. Since 1/3 were sold, 2/3 remain of 45.
2/3 of 45 is 30

30 houses are left to be sold

A line passes through the points (4, 4) and (6, 10). What is its equation in slope-intercept form?

Answers

Y=3x-8 is the correct answer

Riley is saving up to buy a new television. She needs a total of $1,164.38. Riley has saved $200.66 already and earns $80.31 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?

Answers

1. First we can subtract $200.66 from $1,164.38 to find how much Riley has left to save: $963.72

2. Now we can divide $963.72 by how much Riley earns in a week $80.31 to find the number of weeks: 12 weeks

Answer: 12 weeks

Hope this helps!

GIVING BRAINLIEST

Wynter likes to take the long way to school each morning. He walks 4 blocks south and then 4 blocks west to arrive at the school. Today he is running late and decides go directly to school to save time. (Assume there is nothing obstructing his path.) If one block is 320 feet, how many feet will he travel if he goes directly to school? Round to the nearest tenth of a foot.

Answers

Answer:
Distance travel by Drew = 1,315.21 feet (Approx)
Step-by-step explanation:
Given:
Total block in north = 3
Total block in west = 3
1 block = 310 feet
Find:
Distance travel by Drew
Computation:
Total distance in north = 3 × 310 = 930 feet
Total distance in west = 3 × 310 = 930 feet
Distance travel by Drew = Total distance in
north? + Total distance in west?
Distance travel by Drew = v9302 + 9302
Distance travel by Drew:
= V864,900 + 864,900
Distance travel by Drew = V1,729,800
Distance travel by Drew = 1,315.21 feet (Approx)

Distance travel by Drew = 1,315.21 feet (Approx)

What is distance?

Distance is a measure of how far apart two objects or locations are using numbers. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. Sometimes, the symbol |AB| is used to represent the distance between two points.

Given:

Total block in north = 3

Total block in west = 3

1 block = 310 feet

Find:

Distance travel by Drew

Computation:

Total distance in north = 3 × 310 = 930 feet

Total distance in west = 3 × 310 = 930 feet

Distance travel by Drew = Total distance in

north? + Total distance in west?

Distance travel by Drew = v9302 + 9302

Distance travel by Drew:

= V864,900 + 864,900

Distance travel by Drew = V1,729,800

Distance travel by Drew = 1,315.21 feet (Approx)

to learn about distance refer to:

https://brainly.com/question/11945643

#SPJ2

the perimeter of an equilateral triangle is 14.4 cm. Find out the length of the side of that triangle in decimal fraction. (step by step)​

Answers

Answer:

43.2 is the correct answer happy

Helppppp it's due todayyyyyyyy.​

Answers

Answer:

65.1mm

Step-by-step explanation:

(4*3+4*3+5.7*3/2)*2

(12+12+8.55)*2

32.55*2

65.1mm

!20 points! Here are two expressions whose product is a new expression, A:

Answers

Answer:

Whats A?

Step-by-step explanation:

Simplify the expression 4x^3x2x^3

Answers

8x^4 is the answer
(4×2)x^2x^2
8x^2x^2
8x^2+2= 8x^4


Divide 31.50 / 2.50 step by step. Write is out on paper if you can. :D

Answers

Answer:

12.6 you divide 31.50 by 2.50 pretend the decimal signs aren't there.

2p+3q=-7
3p+5q=-12
What is the solution in an ordered pair?

Answers

Answer:

(p, q ) = (1, - 3 )

Step-by-step explanation:

2p + 3q = - 7 → (1)

3p + 5q = - 12 → (2)

Multiplying (1) by 3 and (2) by - 2 and adding the result will eliminate p

6p + 9q = - 21 → (3)

- 6p - 10q = 24 → (4)

Add (3) and (4) term by term to eliminate p

0 - q = 3

-q = 3 ( multiply both sides by - 1 )

q = - 3

Substitute q = - 3 into either of the 2 equations and solve for p

Substituting into (1)

2p + 3(- 3) = - 7

2p - 9 = - 7 ( add 9 to both sides )

2p = 2 ( divide both sides by 2 )

p = 1

True or False:
Rachel used 12 centimeters of tape to wrap 3
presents.
Her unit rate is 12.
Select one:
True
O False
Check
No links.

Answers

Answer:

False

Step-by-step explanation:

The unit rate should be 9

Answer:

i think false

Step-by-step explanation:

if im wrong forgive if am right brainliest pls:)

What is the slope of the line?
3x-4y=73x−4y=7

Answers

Answer:

67x-7y2x-f8

Step-by-step explanation:

What is the slope of the line passing through the points (−3, 4) and (2, −1)?

3/5 this is a fraction by the way

1

−1

−53

Answers

[tex](x_1,y_1) = (-3,4),~~ (x_2,y_2) = (2,-1)\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} =\dfrac{-1-4}{2+3} = \dfrac{-5}5 = -1[/tex]

I desperately need this answer. Thank You so much and have a great day

Answers

Answer:

D

Step-by-step explanation:

p(t)=2t+5

p(10)=2(10)+5

p(10)=20+5

p(10)=25

please give me a brainliest since this took a lot of thinking

!!Help!!
solve for x​

Answers

WXY = XYW ( = 41 ) ⇒  XYW is a isosceles triangle

⇒ XW = YW

⇒ 54 = 6x + 6

⇒ 6( x + 1 ) = 54

⇒ x + 1 = 9

⇒ x = 8

ok done. Thank to me :>

Ashely burns 0.48 calories for every 20 feet she runs.How many calories would she burn after running 2 miles?

Answers

Answer:

253.44 calories

Step-by-step explanation:

2 miles = 10560 feet

10560/20 = 528

528 · 0.48 = 253.44

calls for
1
4
4
1

cup of sugar and
2
3
3
2

cup of flour. Janelle wants to proportionally increase these amounts to get a new recipe using one cup of sugar.

Answers

Answer:

Use a converation table and figure out 4/4-1/4 and that would be how much you would add for a new cup of sugar

The median of the observations, 8,11,15, x +1, X +3, 30, 35, 40, 43, Arranged in ascending Order in 22 Find the value of x

Answers

Middle terms are x+1 and x+3

(X+1+x+3)/2= 22

2x+4 = 44

2x = 40

X = 20

PLS HELP ASAP PLS I RLLY NEED HELP.

Answers

Answer:

THE ANWSER IS A

Step-by-step explanation:

YOU JUST DEVIDE THE REGULAR FRACTION AND PUT IT IN ORDER FROM THERE

Other Questions
government organs that are responsible for supervising these daily migrations Question 3Find the Slope.(2,8) and (4, -3) Blau and Duncan developed a status attainment model, which is a more flexible approach to studying social mobility than are mobility tables. The reason a status attainment model is more flexible is because it Accessing logarithmic Matrix..Terminal sequence pairs = 1 0 - 83 - 32 5 - 128 An initially stationary object experiences an acceleration of 6 m/s2 for a time of 15 s. How far will it travel during that time?Free-fall Acceleration is -10 m/s^2 Which of the following correctly describes one way that cellular respiration contributes to the carbon cycle?Choose 1 answer:Choose 1 answer:(Choice A)ACellular respiration breaks down carbon-based molecules and releases oxygen into the atmosphere.(Choice B)BCellular respiration takes carbon dioxide from the atmosphere and uses it to make carbon-based molecules that are stored as biomass.(Choice C)CCellular respiration helps move carbon from the bodies of living organisms into the atmosphere. 1. Rocky Mountain spotted fever is a bacterial infection transmitted by a tick. What type of symbiosis occurs between a deer and the tick?A. MutualismB. CommensalismC. Parasitism2. The oxpecker is a bird that eats the insects off the back of a zebra or rhino? What type of a symbiotic relationship is this?A. MutualismB. CommensalismC. Parasitism3. Humans have good bacteria in their digestive tract, which assists in digesting food. The bacteria thrive there. What type of a symbiotic relationship is this?A. MutualismB. CommensalismC. Parasitism4. Barnacles attach themselves to whales in order to be where food is available and also for transportation. This does not hurt the whale? What type of a symbiotic relationship is this?A. MutualismB. CommensalismC. ParasitismMutualism examples Cules de las caractersticas que destacan a la burguesa media consideras negativas? Por qu? Help would be greatly appreciated!!Multiply as indicated. Write the product in standard form.(1+3i)(-3-i)Thanks to whoever helps in advance!! What is 7536 to 1 significant figure Choose the verb:MaryQuicklyRanAway Epilogue Context: European Cultural Change: The Age of Exploration resulted in a steep increase in the variety of goods available in Europe. Suddenly, items from around the world were available in Europe in ever-increasing quantities. This resulted in changing patterns of consumption for all classes of European society, especially the newly rich middle class. Demand increased for luxury goods that could be used to display wealth and status, especially goods from China and India. Things which in centuries past were considered to be quite rare are now thought by all and sundry to be quite necessary. Ralph Fitch, British merchant, 1599.Explain what Ralph Fitch means when he stated Things which in centuries past were considered to be quite rare are now thought by all and sundry to be quite necessary. Be specific. Conner has $3 more than chi and $2 more than Cher Jan has &1 less than Cher together they have $28 how much does Conner have please help me out ill give brainlist Which actions are involved in the immune response?regulating hormonal and autonomous responsesidentifying and destroying harmful substancesincreasing and supporting the ability of red blood cells to carry oxygenregulating and adjusting the skin's secretion of sweat and oil Describe the roles of East African men and women in agriculture. Which of the following elements has the lowest first ionizition energy ? 1 ) Li 2)Mg 3) Na 4) Al helpppppppppppppppppppppppppppA machine cuts a strip of carpet into two pieces. The length of the smaller piece is 5 meters greater than 1/4 the length of the larger piece. If the length of the smaller piece is 12 meters, the length of the bigger piece is _____________ meters and the total length of the carpet is _____________ meters. what did nineteenth-century american expansionists mean by the term manifest destiny? Question involving derivatives and limits...What is the limit as x approaches 2 of (3 f(x) - 15) / (x-2)... where f(2) is 5. The answer is not 0, I checked.the derivative f'(2) is 1/8 in case that's neededit can be either 3/8, , 3.545, or 3/2