Let f(x) = x+2/x+6
f^-1(-6) =

Let F(x) = X+2/x+6 F^-1(-6) =

Answers

Answer 1

We can explicitly find the inverse. If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then

[tex]f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x[/tex]

Solve for the inverse :

[tex]\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x[/tex]

[tex]\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x[/tex]

[tex]1 - \dfrac4{f^{-1}(x) + 6} = x[/tex]

[tex]1 - x = \dfrac4{f^{-1}(x) + 6}[/tex]

[tex]f^{-1}(x) + 6 = \dfrac4{1-x}[/tex]

[tex]\implies f^{-1}(x) = \dfrac4{1-x} - 6[/tex]

Then when x = -6, we have

[tex]f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}[/tex]

Alternatively, we can first solve for x such that [tex]f(x) = -6[/tex]. Then taking the inverse of both sides, [tex]x = f^{-1}(-6)[/tex]. (The difference in this method is that we don't compute the inverse for all x.)

We have

[tex]\dfrac{x+2}{x+6} = -6[/tex]

[tex]x + 2 = -6 (x + 6)[/tex]

[tex]x + 2 = -6x - 36[/tex]

[tex]7x = -38[/tex]

[tex]\implies x = \boxed{-\dfrac{38}7}[/tex]


Related Questions

After sitting in a refrigerator for a while, a turkey at a temperature of 34^\circ34

F is placed on the counter and slowly warms closer to room temperature (67^\circ67

F). Newton's Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the room, as given by the formula below:
T=T_a+(T_0-T_a)e^{-kt}
T=T
a

+(T
0

−T
a

)e
−kt

T_a=T
a

= the temperature surrounding the object
T_0=T
0

= the initial temperature of the object
t=t= the time in minutes
T=T= the temperature of the object after tt minutes
k=k= decay constant

The turkey reaches the temperature of 45^\circ45

F after 15 minutes. Using this information, find the value of kk, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 60 minutes.

Enter only the final temperature into the input box.

Answers

The temperature of the body after 60 minutes is  60.5° F.

Using the Newton's law of cooling;

T(t) =[tex]Ts + (To - Ts)e^-kt[/tex]

T(t) = temperature at time t

Ts = temperature of the surrounding

To = Temperature of object

t = time taken

k = cooling constant

Now;

[tex]T(t) -Ts=(To - Ts)e^-kt\\45 - 67 = (34 - 67)e^-15k\\-22 = -33e^-15k\\-22/-33 = e^-15k\\0.667 = e^-15k\\ln(0.667) = ln( e^-15k)\\-0.405 = -15k\\k = -0.405/ -15\\k = 0.027[/tex]

At t = 60 min

[tex]T(t) = Ts + (To - Ts)e^-ktT(60) = 67 + (34 - 67)e^-( 0.027*60)\\T(60) = \\67 + (-33)e^-( 0.027 * 60)\\T(60) = \\60.5 F[/tex]

T(60) = 60.5° F

Learn more about Newton's law of cooling: https://brainly.com/question/13748261

Answer:

T≈169

Step-by-step explanation:

Enter only the final temperature into the input box.

T_a = 67\hspace{50px}T_0=210

T  

a

=67T  

0

=210

\text{Write Formula:}

Write Formula:

T=67+(210-67)e^{-kt}

T=67+(210−67)e  

−kt

 

Plug in givens

\color{blue}{T}=67+143e^{-k\color{green}{t}}

T=67+143e  

−kt

 

Simplify

\text{Plug in given time and temperature:}

Plug in given time and temperature:

\color{blue}{193}=67+143e^{-k(\color{green}{1.5})}

193=67+143e  

−k(1.5)

 

Simplify

\text{Solve for }k\text{:}

Solve for k:

193=

193=

\,\,67+143e^{-1.5k}

67+143e  

−1.5k

 

-67\phantom{=}

−67=

\,\,-67

−67

126=

126=

\,\,143e^{-1.5k}

143e  

−1.5k

 

\frac{126}{143}=

143

126

=

\,\,\frac{143e^{-1.5k}}{143}

143

143e  

−1.5k

 

 

Divide by 143

0.8811189=

0.8811189=

\,\,e^{-1.5k}

e  

−1.5k

 

\ln\left(0.8811189\right)=

ln(0.8811189)=

\,\,\ln\left(e^{-1.5k}\right)

ln(e  

−1.5k

)

Take ln of both sides

\ln\left(0.8811189\right)=

ln(0.8811189)=

\,\,-1.5k

−1.5k

\frac{\ln\left(0.8811189\right)}{-1.5}=

−1.5

ln(0.8811189)

=

\,\,\frac{-1.5k}{-1.5}

−1.5

−1.5k

 

Divide by -1.5

0.0843751=

0.0843751=

\,\,k

k

k\approx

k≈

\,\,\color{blue}{0.084}

0.084

Round k to nearest thousandth

\text{Complete Formula:}

Complete Formula:

T=67+143e^{-\color{blue}{0.084}t}

T=67+143e  

−0.084t

 

Plug in k

\text{Find temperature after }\color{green}{4}\text{ minutes:}

Find temperature after 4 minutes:

T=67+143e^{-0.084(\color{green}{4})}

T=67+143e  

−0.084(4)

 

Plug in time

T=67+143e^{-0.336}

T=67+143e  

−0.336

 

Multiply

T=169.1911041

T=169.1911041

Plug into the calculator

T\approx 169

T≈169

A book store is hosting a special night in which familles can enjoy a story and craft time. Tickets to the event must be bought ahead of time and are $1.50 for children and $2.50 for adults. So far, 45 children's tickets have been sold, which is 60% of the total tickets sold. How many tickets have been sold so far? Show or explain how you got your answer.steps please​

Answers

Answer:

45

Step-by-step explanation:

just typing this so I'll have 20

What are the coordinates of B

Answers

Answer: (-7,-5)

Step-by-step explanation:

Because when you mark point M and A if you mirror point M and A on the x Axis then you will get (-7,-5)

12 degree C fell to -5 degree C WHAT IS THE DIFFERENCE

Answers

Answer:

7

12-5=6 this helps you''';

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)

Answers

Answer:

[tex]I(-2,0) \to\\ I \ ' \ (-0.5,0)\\\\J(3,2) \to\\ J \ ' \ (0.75,0.5)\\\\K(1,-1) \to\\ K \ ' \ (0.25,-0.25)\\\\[/tex]

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

Explanation:

For each point, multiply each x,y coordinate by 0.25 (the scale factor) to dilate the preimage to the image. This will shrink the image because the positive scale factor is less than 1.

So for instance, point J(3,2) will have this scratch work

3*(0.25) = 0.752*(0.25) = 0.5

meaning J(3,2) moves to J ' (0.75, 0.5)

----------

Side notes:

0.25 = 1/40.5 = 2/4 = 1/20.75 = 3/4this trick only works if the center of dilation is the origin


A choir teacher is dividing 48 sopranos and 32 altos into singing groups. He wants each
group to have the same combination of sopranos and altos, with no singers left over. What is
the area

Answers

Answer:

32

Step-by-step explanation:

x(48 - 2x) = 32

Hope it helps.

Solve for x.
9x + 1 = 7x - 8x + 4

Answers

Answer:x = 3/10Step-by-step explanation:9x + 1 = 7x - 8x + 4=> 9x + 1 = -x + 4=> 9x + x = 4 - 1=> 10x = 3=> x = 3/10Conclusion:

Therefore, the answer is 3/10.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

9x + 1 = 7x - 8x + 4

9x + 1 = -x + 4

9x + 1 - 1 = -x + 4 - 1

9x = -x + 3

9x + x = -x + 3 + x

10x = 3

x = 3/10

Apollo110

Can y’all please help me with these questions

Answers

Answer:

13. STR

14. VY

Step-by-step explanation:

I hope this helps!

Help.............???!!!

Answers

Answer:

Its either A or C

Step-by-step explanation:

2,983,562 to the nearest hurdreth

Answers

2,983,600 is your answer to the nearest hundred

Answer:

2,983,562 if you mean hundredth

if to the nearest hundred then 2,983,600

Step-by-step explanation:

the graph shows the volumes of petrol and diesel delivered in the Uk between 1970 and 2012

Answers

Answer:

whats the question.

Step-by-step explanation:

solve the compound inequality 2(x-2)+7>-1 and 5-4x>9

Answers

Answer:

1) x > -2

2) x < -1

Step-by-step explanation:

1) 2(x - 2) + 7 > -1

2x - 4 + 7 > -1

2x + 3 > -1

2x > -4

x > -2

2) 5 - 4x > 9

-4x > 4

x < -1

Las medidas de posición dividen una distribución ordenada en grupos con la misma cantidad de datos.

Answers

Answer:

no entiendo tu pregunta xD !?

Answer:HOLA

Step-by-step explanation:Mi casa su casa , come estas , si uno

purchase good from naresh rs 9000 and isued a cheque of rs 4000 only as payment​

Answers

Answer:

that means you have a 5000 dollar debt

Hope This Helps!!!

Find the least common denominator for these fractions. Enter your answer in
the space provided.

Answers

Answer:

10

Step-by-step explanation:

"Least" means smallest.

"Common" means same.

"Denominator " means the bottom number in a fraction.

Something/2 can be changed to something/10

AND something/5 can also be changed to

something/10

1/2 >>>> 5/10

3/5 >>>> 6/10

10 is the least common denominator.

help me please please​

Answers

Answer:

i think its D or 14/16

Step-by-step explanation:

Answer:

[tex]\frac{14}{16}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}[/tex] + [tex]\frac{10}{16}[/tex]

Before adding we require the denominators of both fractions to be common

Multiply numerator/ denominator of first fraction by 4

= [tex]\frac{1(4)}{4(4)}[/tex] + [tex]\frac{10}{16}[/tex]

= [tex]\frac{4}{16}[/tex] + [tex]\frac{10}{16}[/tex] ( now add the numerators leaving the common denominator )

= [tex]\frac{4+10}{16}[/tex]

= [tex]\frac{14}{16}[/tex]

The fraction can be simplified by dividing the numerator/ denominator by 2 to

[tex]\frac{7}{8}[/tex]

71.841 to the nearest tenth

Answers

Answer:

71.8

Step-by-step explanation:

71.841:

The 4 represents the number that we'll be looking at since 4 is the next position to the right of 8, 8 is in the Tenths place. 4 is in the Hundredths place, and 4 will be the only number that could round up the 8.

How?

In order to round, we need to remember how to round numbers:

If the digit is less than 5, the number to the left stays the same.If the digit is greater than, or equal to 5, the number to the left rounds up, or increases by 1.

Solve:

First, 4<5, meaning that 4 is less than 5.

#1 above is stating that the number to the left of 4 stays the same.

If we use that rule:

71.8 is our answer.

A car traveled 133 miles in 4 3/4 hours. What was the cars average speed in miles per hour?

Answers

4 3/4 = 19/4

 

133/(19/4) = 133(4/19) = 1197/19 = 63 mph

Fill in the missing numbers below.

5 feet + 12 inches = blank
yard(s)

Blank inches = 1 foot + 1 yard


Blank feet = 3 feet + 24 inches

Answers

Answer:

5 feet + 12 inches = 2 yards

48 inches = 1 foot + 1 yard

5 feet = 3 feet + 24 inches

Step-by-step explanation:

To help solve these equations, you must know how to convert feet to inches, inches to yards, etc. Use the information below:

1 feet = 12 inches

3 feet = 1 yard

To solve 5 feet + 12 inches = blank yard(s), convert 5 feet & 12 inches to yards. Since 5 feet would be complicated to convert, let's convert 12 inches to feet first.

12 inches = 1 feet

Instead of 12 inches, we can substitute it as 5 feet + 1 feet = blank yard(s). That would be 6 feet = ? yards. 3 feet = 1 yard, which tells us we must divide both sides by 3. Thus, 5 feet + 12 inches = 2 yards.

Blank inches = 1 foot + 1 yard

To find the # of inches in a yard, you must first know that 3 feet = 1 yard. If there are 12 inches in a foot, we must multiply 3 by 12, getting us 36. You add 12 inches (1 foot), getting us 48 inches in total. Thus 48 inches = 1 foot + 1 yard.

Blank feet = 3 feet + 24 inches

Since 3 feet is already feet, we do not need to convert it. If 12 inches is 1 foot, we must divide 24 inches by 12. So, there is 2 feet in 24 inches. 2 + 3 is 5. Thus, 5 feet = 3 feet +24 inches.

Describe how to find all the points on a baseball field that are equidistant from second base and third base.

In the figure, m∠DBE=50. Find each of the following.

m∠BEDm angle b e d
m∠BEAm angle b e eh
x
y
BE
BC

Answers

From the given diagram, the following statements are true:

AB = BC

3y = 5y - 22

3y - 5y = -22

-2y = -22

y = 11

Similarly, m<DBE = 50 degrees

m<BED = 90 - m<DBE

m<BED = 90 - 50

m<BED = 40 degrees

Since BE = BC = 3y

BE = BC = 3(11) = 33

Also, 7x  - 2 = 40

7x = 40 + 2

7x = 42

x = 6

Get the measure of m<BEA

m<BEA = 7x - 2

m<BEA = 7(6) - 2

m<BEA = 40 degrees

Learn more on angles here: https://brainly.com/question/16281260

50 mm = how many cm?

Answers

Answer:

5cm

Step-by-step explanation:

50mm ÷ 10 = 5cm

7) If a point is randomly chosen on the square shown, what is the probability that it will be in the red section of the figure? A) 1/4 B) 1/3 C) 1/2 D) 3/4

Answers

Image is blurry. Please reupload

Answer:

1/4

Step-by-step explanation:

1/4 because it is one piece out of the four cuts. if it were yellow, than it would be 2/4, or 1/2

A company has two large computers. The slower computer can send all the company’s email in 50 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?

Answers

Answer:

18 minutes and 45 seconds

Step-by-step explanation:

[tex]\frac{1}{50}[/tex] + [tex]\frac{1}{30}[/tex] = [tex]\frac{3+5}{150}[/tex] = [tex]\frac{4}{75}[/tex]

1 ÷ [tex]\frac{4}{75}[/tex] = [tex]\frac{75}{4}[/tex] = 18' 45''

Answer:

18.75 minutes If A and B work together

-6x+6y=9 (1/2,2) please helppppp

Answers

Answer:

A. Solution

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinate Planes

Coordinates (x, y)

Step-by-step explanation:

*Note:

A coordinate is a solution if both the left side and right side of the equation is equal.

Step 1: Define

Identify.

-6x + 6y = 9

(1/2, 2)

Step 2: Verify

Substitute in variables [Equation]:                                                                   -6(1/2) + 6(2) = 9[Order of Operations] Evaluate:                                                                      9 = 9

Since 9 does indeed equal 9, the coordinate (1/2, 2) is a solution.

If f(1) = 9 and f(n) = -4f(n-1) + 4 then find the value of f(3).

Answers

Answer:

132

Step-by-step explanation:

f(1) = 9

f(n) = -4f(n-1) + 4

Let n = 2

f(2) = -4f(2-1) + 4 = -4 f(1) +4 = -4(9) +4 = -36+4 = -32

Let n = 3

f(3) = -4f(2-1) + 4 =-4f(2)+4 =  -4 (-32) +4 = 128+4=132

what is the complete factorization of the polynomial below
[tex] {x}^{3} - {2x}^{2} + x - 2[/tex]


[tex]a. (x - 2)(x + i)(x - i)[/tex]
[tex]b.(x + 2)(x - i)(x - i)[/tex]
[tex]c.(x + 2)(x + i)(x - i)[/tex]
[tex]d.(x - 2)(x - i)(x - i)[/tex]

Answers

Answer:

[tex]a. \ (x-2)(x+i)(x-i)[/tex]

Step-by-step explanation:

First of all let's notice that [tex](x-i)(x-i)=(x-i)^2 = x^2+2xi-1 \in \mathbb{C}[/tex] while our original polynomial is real. So we can rule out the even options B and D. At this point, if the polynomial has a factor of [tex](x-\alpha)[/tex] it means tha [tex]\alpha[/tex] is a zero of the polynomial. Let's check both 2 (for option a) and -2 (for option c)

[tex]p(2)=2^3-2(2)^2+2-2= 8-8+2-2=0[/tex]

[tex]p(-2)= (-2)^3-2(-2)^2+(-2)-2=-8-8-2-2=-20[/tex]

At this point 2 is a zero, and our final factoring is a[tex](x-2)(x+i)(x-i)[/tex]

Please help me in this!!!!

Answers

Step-by-step explanation:

you really don't see this ?

this is rotated by 180 degrees around the origin.

do you see how the different points change positive from one shape to the other ?

think what happens when you rotate a disk (like a plate) with something on it. how does that something on it change is position and orientation ?

this here is the same thing. look at H and how it turns into O.


Please help me I don’t want to fail

Answers

Answer:

c

Step-by-step explanation:

In a parking lot,there are 16 silver cars, 8 blue cars ,and 10 red cars . A car leaves the parking lot. What is the probability that it is
a: a silver car?
b: a blue car?
c: a red car?
d: suppose that the first car that leaves is a silver car . What is the probability that the second car that leaves is not a silver car?

Answers

Answer:

a) 8/17

b) 4/17

c) 5/17

d) 48/187

Step-by-step explanation:

a) P(silver) = 16/34 = 8/17

b) P(blue) = 4/17

c) P(red) = 5/17

d) P(silver, not silver) = 8/17 × 18/33 = 144/561 = 48/187

The probability for each event are -

[A] -  8/34

[B] -  16/34

[C] -  10/34

[D] -  18/33

What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -  

        P(A) = n(A)/n(S)

        where -

        n(A) = Number of outcomes favorable to event A.

       n(S) = Total number of outcomes

We have 16 silver cars, 8 blue cars and 10 red cars in a parking lot.

[A] -

P{silver} = 8/(16 + 8 + 10) = 8/34

[B] -

P{blue} = 16/(16 + 8 + 10) = 16/34

{C} -

P{red} = 10/(16 + 8 + 10) = 10/34

D) -

P{not silver} = 1 - 15/33 = 18/33

Therefore, the probability for each event are -

[A] -  8/34

[B] -  16/34

[C] -  10/34

[D] -  18/33

To solve more questions on Probability, visit the link below -

brainly.com/question/24028840

#SPJ2

3. My divisor is 8.
I am less than 30.
I am greater than 3 X 8.
My remainder is 5.
What dividend am I?

Answers

Answer: 29

Step-by-step explanation:

29 ÷ 8 = 3 remainder: 5

I solved using long division.

Answer:

29

Step-by-step explanation:

30

24

5

8x3=24

24+5= 29

Beacuase it had to be smaller than 30

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