How to find the inverse of f(x) = -(3/-x-3) - 2

Answers

Answer 1

so, to get the inverse relation of anything, as you'd already know, we first do a quick switcharoo on the variables, and then solve for "y".

[tex]\bf \stackrel{f(x)}{y}=-\cfrac{3}{-x-3}-2\qquad inverse\implies \boxed{x}=-\cfrac{3}{-\boxed{y}-3}-2 \\\\\\ x+2=\cfrac{3}{-(-y-3)}\implies x+2=\cfrac{3}{y+3}\implies (x+2)(y+3)=3 \\\\\\ xy+3x+2y+6=3\implies xy+2y=3-3x-6 \\\\\\ y(x+2)=-3x-3\implies y=\cfrac{-3x-3}{x+2}\implies \stackrel{f^{-1}(x)}{y}=\cfrac{-3(x+1)}{x+2}[/tex]

Answer 2

The inverse is f⁻¹(x) = -3(x + 1)/(x + 2).

To find the inverse of the given function f(x), follow these steps:

Replace f(x) with y: y = -(3/(-x-3)) - 2Swap x and y to start finding the inverse: x = -(3/(-y - 3)) - 2Isolate the term with y: x + 2 = -(3/(-y - 3))Multiply both sides by (-y - 3) to get: (x + 2)(-y - 3) = -3Distribute x + 2: -xy - 3x - 2y - 6 = -3Collect y terms on one side: -xy - 2y = 3x + 3Factor out y: y(-x - 2) = 3(x + 1)Solve for y: y = -3(x + 1)/(x + 2)

Thus, the inverse function is f⁻¹(x) = -3(x + 1)/(x + 2).

Related Questions

an air traffic controller is tracking two planes. To start, playing a is at an altitude of 2814 ft and plan B is just taking off. Plan a is gaining altitude at 30.5 feet per second in playing day is gaining altitude at 80.75 feet per second. How many seconds will pass before the planes are on the same altitude

Answers

Model the altitude of each plane with a linear equation.
The initial altitude is the 'y-intercept'.
The rate of elevation is the slope.

Plane A: y = 30.5x + 2814

Plane B: y = 80.75x

The planes will be at same altitude when the y values are equal.
80.75x = 30.5x + 2814

Solve equation for 'x'.
80.75x - 30.5x = 2814
50.25x = 2814
x = (2814/50.25) = 56

Answer:
It will take 56 seconds before planes are at same altitude.

Answer:

56 seconds will pass.

Step-by-step explanation:

Because its right. :)

please give brainliest

Ken watches a marching band. He sees 2 rows of flute players. Six people are in each row. He sees 8 trombone players. How many flute or trombone players does Ken see

Answers

Twelve flute players.

Eight trombone players.

20 total of flute and trombone players.

The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card

Answers

To set up an equation for this you must know what needs to be on the other side of the equals sign or what the answer is supposed to be. In this case, we know the answer should be the money remaining on the card. Since there is no number value for this, you must pick a variable to represent it. I am going to use variable R. So, since we know that you start with 100 dollars, and lose 4 dollars for each lunch, we can tell that there will be subtraction taking place. We also do not know how many lunches have been bought so we need a variable for that too. I will use variable x. That will leave you with an equation of:
R = 100 - 4x

x= number of lunches bought
R= remaining money on the lunch card

Hope this helps!

Harrison mows lawns and rakes leaves for his summer and fall weekend jobs. He gets $10 an hour to mow lawns and $8 an hour to rake leaves. If, during September, Harrison mows for m hours and rakes for 12 hours, which expression represents the amount of money he makes? Harrison mows lawns for 11 hours, so m = 11. How much money does he make in September?

Answers

total money= 10m+8(12)

Answer:

first one is 10m+8(12)

second one is 206

Step-by-step explanation:

i took it alrr..

jackson made 15 calls in 20 minutes. how many calls per minute did he make

Answers

i think it's .75...:')

Hello User :)

How are you doing?
In this case, your trying to find how many calls he makes per minute. So here we go! We know he made 15 calls in 20 minutes! Therefore, we must divide to find the unit number, which basically is "Numbers Simplified."

[tex]15 / 20=0.75[/tex]

That means he makes 0.75th of a call in 1 minute.

the table shows the low temperature in five cities on a winter day. which statement is true

A. it is warmer in Tacoma than in Roseville

B. it is colder in Roseville Than in Helena

C. It is warmer in Helena than in Fargo

D. it is colder in Tacoma than in Great Falls

Answers

The answer to that question so D because 1.0 is the lowest tem.

Find the roc of the volume of a cube with respect to the length of its side s

Answers

If the length of one side of a cube is s, then the derivative of the formula for the volume of the cube is

dV/ds = 3s^2.

The roc of the volume of a cube with respect to the length of its side s is 3s².

What is rate of change?

The rate of change of a function is the rate at which the output values change over the input value.

The rate of change of a function is one degree less than the actual function.

The volume of a cube is :

V = s³

The rate of change of volume V with respect to length a will be :

dV/ds = d(s³ )/ds

= 3s²

This means that, a cubic function will have a quadratic rate of change

Hence, The roc of the volume of a cube with respect to the length of its side s is 3s².

Answers

P-2c/2 = D So, P-2c all over 2 is equal to D.

Answer: D = (P - 2C)/2

Step-by-step explanation:

We want to solve P= 2D + 2C for D

This means "isolate D in one side of the equation"

The first step is subtracting 2C in the both sides of the equation:

P - 2C = 2D + 2C - 2C = 2D

P - 2C = 2D

Now, we want to take of the multiplication that is acting on D, so we divide in both sides by 2:

(P - 2C)/2 = (2D)/2 = D

Now we have D isolated, and this is:

D = (P - 2C)/2

If there were a million cars in line, bumper to bumper, with a average length of 10.14 feet, how long would that line be in miles? (Round to the nearest mile)

Answers

The answer is 10,140,000fett because 10.14(the length of each car) times 1,000,000 is 10,140,000

1,920 miles long

Hope this helps : )

Find the distance between points M(6,16) and Z(-1,14) to the nearest tenth.

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) M&({{ 6}}\quad ,&{{ 16}})\quad % (c,d) Z&({{ -1}}\quad ,&{{ 14}}) \end{array}\quad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ MZ=\sqrt{(-1-6)^2+(14-16)^2}\implies MZ=\sqrt{(-7)^2+(-2)^2} \\\\\\ MZ=\sqrt{49+4}\implies MZ=\sqrt{53}\implies MZ\approx 7.3[/tex]

Suppose a and b are 3x3 matrices, with det(a) = 5 and det(b) = 3.
a. det(2a) = ? 4 pts
b. det((ab)-1) = ?

Answers

[tex]\det(2\mathbf A)=2^3\det\mathbf A=8\times5=40[/tex]

[tex]\det(\mathbf{AB})^{-1}=\dfrac1{\det\mathbf{AB}}=\dfrac1{\det\mathbf A\det\mathbf B}=\dfrac1{5\times3}=\dfrac1{15}[/tex]

If a production line produces 50 mouse traps every 30 minutes over the course of a 10-hour work day with a half hour break for lunch how many mouse traps are made in a day

Answers

950 mouse traps

100 traps/ 1 hr times 9.5 hrs = 950

50 mouse traps every 30 minutes.....double that and u get 100 mouse traps per hr.

10 hrs - half hr break (30 minutes) = 9.5 hrs of work

so if it is 100 mousetraps per hr...and the hrs worked are 9.5 hrs.....then the number of mousetraps produced are : 9.5 * 100 = 950 mouse traps <==

What is "The sum of m and n"

Answers

3x-x+2=4...this is your answer to this question

m + n, pretty sure since there is no known number for n nor m so you would write it like this. So you would put m + n equals a number. Me and my science partner have carefully dissected this problem.

kayla wrote a three-digit number.the value of the digit in the hundreds place is 6 hundreds. the digit in the tens place is 3 less than the digit in the hundreds place. sum of all three digital is 12.what is kayla number?

Answers

336 is kaylas number, hope this helps

633 is the number

6 is the hundreds place
3 is the number that is 3 less than the hundreds number (6)
6+3=9
12-9=3
3 is your last digit

i hope you understood

Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.

If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least.

Splash of Color will always charge the least.

If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective.

If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA.

If it takes 3 hours to paint the rooms, both companies will charge the same amount.

Answers

Answer:

The correct statements are 1, 3, and 5.

Explanation:

Let's calculate the total cost for each company based on the given information:

For Interior Designs USA:

- Evaluation fee: $60.00

- Labor cost per hour: $35.00

- Total labor cost for 7 hours: $35.00/hour × 7 hours = $245.00

- Total cost = Evaluation fee + Total labor cost = $60.00 + $245.00 = $305.00

For Splash of Color:

- Labor cost per hour: $55.00

- Total labor cost for 7 hours: $55.00/hour × 7 hours = $385.00

Now, let's analyze the statements:

1. If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least. - True. ($305.00 < $385.00)

2. Splash of Color will always charge the least. - False. In this case, Interior Designs USA charges less for 7 hours of work.

3. If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective. - True. As we've seen, Splash of Color charges $55.00 per hour, while Interior Designs USA charges $35.00 per hour plus an initial fee.

4. If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA. - False. Let's calculate:

- Interior Designs USA: $60.00 (evaluation fee) + $35.00/hour × 10 hours = $60.00 + $350.00 = $410.00

- Splash of Color: $55.00/hour × 10 hours = $550.00

Splash of Color charges $550.00 - $410.00 = $140.00 more, not $200. Therefore, this statement is false.

5. If it takes 3 hours to paint the rooms, both companies will charge the same amount. - False. Let's calculate:

- Interior Designs USA: $60.00 (evaluation fee) + $35.00/hour × 3 hours = $60.00 + $105.00 = $165.00

- Splash of Color: $55.00/hour × 3 hours = $165.00

They both charge $165.00, so this statement is true.

So, the correct statements are 1, 3, and 5.

A miner descended 1500 feet into a mine. While in the mine, he then rose 1200 feet and then descended 850 feet. What was the miner's net gain or loss in altitude?

Answers

Call descending a negative number and rising a positive number.
Then add the numbers.

A miner descended 1500 feet into a mine.
-1500 ft

he then rose 1200 feet
+1200 ft

then descended 850 feet
-850 ft

Now add the three numbers:
-1500 ft + 1200 ft + (- 850 ft) = -1150 ft

Since the sum is a negative number, that means
he had a net loss in altitude of 1150 ft.

Compare methods of solving linear equations and methods of solving linear inequalities. what do they have in common? what is different?

Answers

hi hi hi jijhjhjhhjhjhjhjhh

The area of a square garden is 98 meters squared. How long is the diagonal

Answers

Because it is square that means its equal on all sides 98 meters

No se jaja yo también tengo tarea que hacer

The domain for f(x) and g(x) is the set of all real numbers. let f(x) = 3x + 5 and g(x) = x2. find g(x) − f(x). x2 − 3x − 5 3x3 − 5x2 3x2 − 5 x3 − 5

Answers

f (x)=3x+5
g (x)=x^2

g (x)-f (x)=(x^2)-(3x+5)
=x^2-3x-5

1.Find the coordinates of the midpoint of __ given that H (-1,3) and X (7,1).
HX

A.(3,1)
B (0,4)
C(-3,1)
D(-4,0)

2. Find the distance between the points R(0,5) and S(12,3). round the answer to the nearest tenth.

A 10.4
B 16
C 12.2
D 11.8

3. An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85) what is the shortest possible distance for the trip?

A. 165 units
B. 170 units
C. 97 units
D. 169 units

Answers

1. B. 2.C 3.C. these answers are all correct.

Answer:

1. (3, 2)

2. Option C. 12.2

3. Option A. 165 units

Step-by-step explanation:

1. The midpoint of two coordinates (x₁, x₂) and (y₁, y₂) is calculate by,

[tex](x, y) = (\frac{x_{1} + x_{2}}{2},\frac{y_{1} + y_{2}}{2})[/tex]

⇒[tex](x, y) = (\frac{-1 + 7}{2},\frac{3 + 1}{2})[/tex]

Thus (x, y) = (3, 2)

Hence, none of given options are true.

2. The distance between two coordinates is calculate by,

[tex]Distance=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]

⇒ Distance = 12.16 ≈ 12.2 unit

Hence, option (C) is correct.

3. The distance between T(80, 20) and V(110, 85) is comparatively smaller than T(80, 20) and U(20, 60).

Using the Distance formula,

[tex]Distance=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]

Distance between T(80, 20) and V(110, 85) is 71.59 unit

and Distance between U(20, 60) and V(110, 85) is 93.41 unit

So, Airplane firstly go to point V from point T and then point U.

Total shortest distance = 71.60 + 93.40 = 165 unit.

Hence, option (A) is correct.

What's the range of 37000 and 45000

Answers

Range: Subtract 37000 from 45000 and you'll have it.

Tim bought a pen for $2.25, a pencil for $0.59, a notebook for $6.49, and a highlighter for $1.49. He used a coupon that gave him $5.25 off his entire purchase. How much did he spend in total?

Answers

Add together the prices: $10.82. This is reduced by the value of the coupon: 10.82-5.25=$5.57.

rachel's necklace cost 20% more than Tammy's shoes. Bryan' s video game cost 30% more than Rachel's necklace. If Tammy's shoes cost $30.00, what did Brian's video game cost?

Answers

I believe Brian's game would be $46.80
30*20%=6
30+6=36
36*30%=10.80
36+10.80=46.80
hope this helps!

Answer:

46.80

Step-by-step explanation:

Pls brainly I need it so bad I spent 10 minutes of my time to solve this.

What number is 49 less than 78

Answers

If you want to subtract the answer is -29.

The number that is 49 less than 78 is 29.

Which equation has the same solution as 4-2(x-5)-x-19

Answers

i believe the equation with the same solution is -3x-5

The equation 3x - 4 = 2x + 7 has the same solution as 4 - 2(x - 5) = x - 19, with both solutions yielding x = 11.

Let's solve the equation step-by-step: 4 - 2(x - 5) = x - 19

First, expand the left side:
4 - 2x + 10 = x - 19Combine like terms:
14 - 2x = x - 19Move all terms involving x to one side:
14 = 3x - 19Move constant terms to the other side:
33 = 3xSolve for x:
x = 11

Now, let's compare this solution to other given equations:

2(x + 5) = -8
2x + 10 = -8
2x = -18
x = -9 (Not a match)3(x - 3) = 9
3x - 9 = 9
3x = 18
x = 6 (Not a match)x + 2 = 2x - 3
2 = x - 3
x = 5 (Not a match)3x - 4 = 2x + 7
3x - 2x = 7 + 4
x = 11 (Match)

The equation with the same solution as 4 - 2(x - 5) = x - 19 is 3x - 4 = 2x + 7.

Complete question: Which equation has the same solution as 4 - 2(x - 5) = x - 19?

2(x + 5) = -83(x - 3) = 9x + 2 = 2x - 33x - 4 = 2x + 7

is (3,13) a solution of the equation y=4x

Answers

y=4x
13 = 4(3)
13 = 12 ...not true

answer
(3,13) is not a solution of the equation y=4x

No because 13 = 4(3) is not equal. So the answer is no.

A flea weighs 8 decigrams, and an ant weighs 3 milligrams. How much more does a flea weigh than an ant?

Answers

now, a decigram is "deci" one tenth of a gram, 1/10 gram.

whilst a milligram is "milli" one thousandth of a gram, 1/1000 gram

now, the flea is 8 of those decigrams thus is 8 * (1/10) grams

the ant is 3 of those milligrams thus 3 * (1/1000) grams

let's find their difference.

[tex]\bf 8\left( \frac{1}{10} \right)\implies \cfrac{8}{10}\implies \stackrel{decigrams}{\cfrac{4}{5}} \\\\\\ 3\left( \frac{1}{1000} \right)\implies \stackrel{milligrams}{\cfrac{3}{1000}}\\\\ -------------------------------\\\\ \cfrac{4}{5}-\cfrac{3}{1000}\impliedby \textit{our LCD is 1000}\implies \cfrac{(200\cdot 4)-3}{1000}\implies \cfrac{800-3}{1000} \\\\\\ \cfrac{797}{1000}\implies 797\left( \frac{1}{1000} \right)\implies 797~milligrams[/tex]

Answer:

797 milligrams

Step-by-step explanation:

Hope this helps!

Consider the graph of f(x)=1/x. Which functions result in a vertical compression? Check all that apply.
a. g(x)=1/3x
b. g(x)=3/x
c. g(x)= - 3/x
d. g(x)= - 1/3x

Answers

I believe the answer would either be a or b.

Hope this helps!

Answer:

A & D

Step-by-step explanation:

This number represents the number of times the base is used as a factor

Answers

It is the exponent.

The exponent is the number used in a power to represent the number of times the base is used as a power.

For example: 7^2. The number 2 is the exponent and it indicates that the number 7 (which is the base) is used two times as a factor, this is, 7^2 = 7 * 7.

Othe example: 4^6. The exponent 6 indicates that the base 4 is used 6 times as a factor => 4^6 = 4 * 4 * 4 * 4 * 4 * 4.

The mailman delivered a $22 check and 3 - $14 bills today. He also took back 1- $5 bill. What is the total in the mailbox?

Answers

3 Times 14 is 42
42+22 is 64
64-5= 59

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