The inverse of the function f (x) = e^x-e^- x/e^x+e^- x + 2 is given by
a.log (x - 2/x - 1 )^1 2
b.12loge (x - 1/3 - x )
c.&log (x/2 - x )^1 2 &
d.log (x - 1/3 - x )^1 2​

Answers

Answer 1

We're asked to find inverse of the function,

[tex]\longrightarrow\rm{f(x)=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}+2}[/tex]

Take [tex]\rm{y=f(x).}[/tex]

[tex]\longrightarrow\rm{y=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}+2}[/tex]

Subtract 2.

[tex]\longrightarrow\rm{y-2=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}}[/tex]

We apply componendo - dividendo rule.

[tex]\rm{\dfrac{a}{b}=\dfrac{c}{d}\quad\iff\quad\dfrac{b+a}{b-a}=\dfrac{d+c}{d-c}}[/tex]

Thus,

[tex]\longrightarrow\rm{\dfrac{y-2}{1}=\dfrac{e^x-e^{-x}}{e^x+e^{-x}}}[/tex]

[tex]\Longrightarrow\rm{\dfrac{1+(y-2)}{1-(y-2)}=\dfrac{(e^x+e^{-x})+(e^x-e^{-x})}{(e^x+e^{-x})-(e^x-e^{-x})}}[/tex]

[tex]\longrightarrow\rm{\dfrac{y-1}{3-y}=\dfrac{2e^x}{2e^{-x}}}[/tex]

[tex]\longrightarrow\rm{\dfrac{e^x}{e^{-x}}=\dfrac{y-1}{3-y}}[/tex]

[tex]\longrightarrow\rm{e^{2x}=\dfrac{y-1}{3-y}}[/tex]

[tex]\longrightarrow\rm{(e^x)^2=\dfrac{y-1}{3-y}}[/tex]

Take square root.

[tex]\longrightarrow\rm{e^x=\sqrt{\dfrac{y-1}{3-y}}}[/tex]

Take natural logarithm.

[tex]\longrightarrow\rm{x=\log_e\sqrt{\dfrac{y-1}{3-y}}}[/tex]

[tex]\longrightarrow\rm{x=\dfrac{1}{2}\log_e\left(\dfrac{y-1}{3-y}\right)}[/tex]

Now take [tex]\rm{x=f^{-1}(y).}[/tex]

[tex]\longrightarrow\rm{f^{-1}(y)=\dfrac{1}{2}\log_e\left(\dfrac{y-1}{3-y}\right)}[/tex]

Replace y by x and finally we get,

[tex]\longrightarrow\rm{\underline{\underline{f^{-1}(x)=\dfrac{1}{2}\log_e\left(\dfrac{x-1}{3-x}\right)}}}[/tex]

This is the inverse of the given function.


Related Questions

How do u make 4.5 m to *what* cm?

Answers

Answer:

To convert any value in meters to centimeters, just multiply the value in meters by the conversion factor 100. So, 4.5 meters times 100 is equal to 450 centimeters.

If you deposited $10,000 in to a bank savings account on your 18th birthday....Said account yielded 3% compounded a nnually, how much money would be in your account on your 58th birthday?

Answers

Answer:

$32600

Step-by-step explanation:

Given data

Principal= $10000

Rate= 3%

Time= 58-18= 40 years

The compound interest expression is

A=P(1+r)^t

Substitute

A=10000(1+0.03)^40

A=10000(1.03)^40

A=10000*3.26

A=$32600

Hence the amount at the 58th birthda is $32600

Help please man please

Answers

Answer: 7

Step-by-step explanation:

Increase 280g in the ratio 5:2​

Answers

Answer:

700

Step-by-step explanation:

Therefore, the increase in 280 in the ratio 5:2 is 700

Use a net to find the surface area of the cone to the nearest
square centimeter. Use 3.14 for it.
23 cm
(The figure is not drawn to scale.)
The surface area of the cone is about cm2.
(Round to the nearest whole number as needed.)

Answers

Answer:

[tex]V=497.16\ cm^3[/tex]

Step-by-step explanation:

The attached figure shows a cone of radius 5 cm and height 19 cm. The formula for the volume of a cone is given by :

[tex]V=\dfrac{1}{3}\pi r^2h[/tex]

Substitute all the values,

[tex]V=\dfrac{1}{3}\times 3.14\times 5^2\times 19\\\\V=497.16\ cm^3[/tex]

So, the volume of the cone is equal to [tex]497.16\ cm^3[/tex].

Ms. Sanchez has $200 to spend on parking and admission to a museum. The parking will cost $10 and admission tickets cost $15.50 per person, including tax. Write and solve an equation that can be used to determine the number of people that she can bring to the museum, including herself.

Answers

Answer:

12 people including herself

Step-by-step explanation:

x = number of people

($200 - $10)/$15.50 = x

x = 12.26

.................................................6y=8x

Answers

Answer: look at the picture

Step-by-step explanation: Hope this help :D

CAN SOMEONE HELP ME PLS TELL ME THE LETTER ANSWER CHOICE!!!!!!!!!!!!!!!!!!!1;))))))))))))))))))))))

Answers

Answer:

C

Step-by-step explanation:

27÷12=2.25

Each gallon costed 2.25$

Please Help!!
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.

Answers

Answer:

15.57

Step-by-step explanation:

I think it is this but I am not sure

Help please ASAP
Give brainiest if correct.

What do I have to do?
The points in the table lie on a line. What is the slope?

Answers

The slope is 1/2, I explain in the other question

What is the solution to the equation: 3x + 5 = 3x − 5

Answers

Answer:

no solution

Step-by-step explanation:

Answer:

the answer is no solution

Step-by-step explanation:

40 POINTS!!!! can you guys please answer these? and make sure they are right!! please hurry im taking this test at the moment!!

Answers

Answer:

1) ?

2) B

3) x = 2*

4) x = 0

5) B

6) y = -5x + 4

7)?

Step-by-step explanation:

1) 5(4x + 2y) - y = 20x + 10y + y = 20x + 9y = 20x + 9y

2)* Any value of  x makes the equation true. All real numbers.  (You may say x = 2 or anything else).

Interval Notation:

(−∞,∞)

BRAINLY TO WHOEVER HELPS

Answers

Answer:

9: D 10: A

Step-by-step explanation:

Answer:

9 is a

Step-by-step explanation:

Can someone help me please

Answers

Answer:

B!

Step-by-step explanation:

Hope this helps :))

Answer:

B) 60 square inches

Step-by-step explanation:

They are asking for the area of the triangle. The formula for area is (length × width) ÷ by 2 = area

so, (8 × 15) ÷ 2 = 60 square inches

4) If there was a coupon for 40% off, what is the final deconstructed
percent written as a DECIMAL? *. A.1.4
B.0.6
C.0.4
D.60%

Answers

Answer:

c

Step-by-step explanation:

Think of it like this. When you convert a percent to a decimal, just put a decimal point before the number. For example, 40%. You would put . before 40, making it 0.40, and you don't need the zero, so it becomes 0.4. For something like 8%, you would first put a zero before the 8, and then put a period before the zero, like so: 8%= 08%=0.08

Here is part of a shopping bill for clothing.



Work out the cost of the jacket before the discount.

Answers

Answer:

how are we supposed to answer this

Answer:

Hewo ❤

Step-by-step explanation:

❤ how are you? ❤

giving brainliest pls answer

Answers

The formula for finding the area of a cone is pi times the radius squared times the height/3. Since we already have the base area, all we need to do is find the height over 3. The height is 6, so 6/3=2. Then 4 pi times 2=8 pi.

The answer is 8pi.

Answer:

8π cubic units

Step-by-step explanation:

V = (4πx 6)/3 = 8π cubic units

Simon bought a 10-pound bag of cat food. He gives his cat 0.3 pound of food per day. Which equation with two variables to describe how the amount of cat food in the bag changes over time.

Answers

Answer:

y = 10 - 0.3t

Step-by-step explanation:

Amount of cat food purchased= 10 pounds

Daily pounds fed to dog = 0.3 pounds

How the amount of cat food in bag changes over time ;

Let y = amount of cat food left in bag

t = number of days since cat food was purchased

Amount of cat food left in bag = amount of cat food purchased - (daily pounds fed to dog * Number of days since cat food was purchased)

y = 10 - 0.3t

Can someone help me? The question is on the image.

Answers

Answer:

top one is 16

bottom one is 9

Step-by-step explanation:

Answer:

the to side length would be 16 and the bottom would be 9

Step-by-step explanation:

Hope this helps :)

9. State Bank pays 5.5 percent interest compounded semiannually on regular
savings accounts. Iva Howe deposited $2,800 in a regular savings account for
2 years. She made no other deposits or withdrawals during the period. How
much interest did her money carn?​

Answers

280 dollars I think

If you do 5.5% x 2year =0.1
2800 x 0.1= 280
Sorry if I'm wrong

Esh deposits $3500 in an account that
earns 3.75% interest each year. After the
first year, Esh has $3631.25 in the account.
After the second year, Esh has $3767.42 in
the account, and after the third year Esh has
$3908.70 in the account.

Answers

Answer:

Compound interest

Step-by-step explanation:

The question requires us to determine if the interest earned is a simple or compound interest

Simple interest = amount deposited x time x interest rate

Future value with compounding = A( 1 + r)^n

A = amount deposited

r = interest rate

n = time

We would calculate the simple interest and the future value in year 2

Simple interest in year 2 = $3500 x 0.0375 x 2 = 262.50

Future value in 2 years with a simple interest = 262.50 + 3500 = $3762.50

Future value in year 2 with compounding = 3500 x (1.0375)^2 = $3767.42

The value provided in year 2 with compounding matches that provided in the question. Thus, it is compounding of interest that is done

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!

Answers

Answer:

Columbian exchange. Tell a story in chronological order of the changes that the community undergoes as it and the communities around it make contact with Europeans over a span of roughly 50 to 100 years.

This section is worth 20 points. See the scoring rubric for more details on how you

will be graded

Use the evidence you gathered to tell the story of a hypothetical indigenous

community in the Americas and its experience involving the Columbian Exchange.

Come up with a community whose circumstances are typical of many in Central

America, the West Indies, or another part of the Americas that had direct contact with

Europeans. Tell the story in chronological order, but feel free to skip whole years or

decades so that you can cover each of the important topics related to the activity: the

availability of goods, the effects of disease, and the impact of European culture

(language and religion, for example), at the very least.

Think of your story as more of a summary than a work of fiction; you must cover a

large span of time in few words. Base the details of the story on factual evidence and

cite your sources, but keep in mind that the text should be written as a story, not as

an essay with a conventional introduction, body, and conclusion. Aim for about 700

to 1,200 words.

free body diagram can be used to help work out the net force acting on an object. True or, false?Columbian exchange. Tell a story in chronological order of the changes that the community undergoes as it and the communities around it make contact with Europeans over a span of roughly 50 to 100 years.

This section is worth 20 points. See the scoring rubric for more details on how you

will be graded

Use the evidence you gathered to tell the story of a hypothetical indigenous

community in the Americas and its experience involving the Columbian Exchange.

Come up with a community whose circumstances are typical of many in Central

America, the West Indies, or another part of the Americas that had direct contact with

Europeans. Tell the story in chronological order, but feel free to skip whole years or

decades so that you can cover each of the important topics related to the activity: the

availability of goods, the effects of disease, and the impact of European culture

(language and religion, for example), at the very least.

Think of your story as more of a summary than a work of fiction; you must cover a

large span of time in few words. Base the details of the story on factual evidence and

cite your sources, but keep in mind that the text should be written as a story, not as

an essay with a conventional introduction, body, and conclusion. Aim for about 700

to 1,200 words.

free body diagram can be used to help work out the net force acting on an object. True or, false?

Step-by-step explanation:

where my brainlest

What is BD?
C
X + 5
B
х
12
27
А
BD =

Answers

This Question Can't be anwsered, Because there is nothing on the right hand side of the equation.

3(x-5)=9 i don't know what to do

Answers

Answer:

x=8

Step-by-step explanation:

3(x-5)=9

3x-15=9

3x-15+15=9+15

3x=24

x=8

Answer:

x=8

Step-by-step explanation:

3(x-5) = 9

(3(x-5))/3 = 9/3

x-5 = 3

x-5+5 = 3+5

x=8

Kaitlin has been given a list of bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?

Answers

Complete question :

Kaitlin has been given a list of 5 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?

Answer:

20 different votes

Step-by-step explanation:

Total number of bands = 5

To select her favorite ; she chooses 1 from the five ;

Number of bands left = 4

From. The 4 she chooses one ; which is her second favorite

Number of different votes possible :

Favorite selection * second favorite selection

(5 * 4) = 20 different votes.

someone help me with math homework

Answers

I hope this helps you

8/4=8/4=18/9=2

Side - Side - Side

Answer:

SSS~

Explanation:

All corresponding sides have the same ratio

Rewrite y= 7/16x+14 in standard form

Answers

Answer:

7x - 16y = -224

Step-by-step explanation:

Standard Form:

Ax + By = C

y= 7/16x+14

-7/16x + y = 14  

(Multiply everything by 16)

-7x + 16y = 224

(Multiply everything by -1)

7x - 16y = -224

Describe how to find the square of -12

Answers

Do you mean findin -12 squared or -12^2?

Help please!! Will mark brainstest!!
Scatter Plot is in the picture.
It says write an equation for the trend line.
A) y=-12.5x+250
B) y=12.5x+250
C) y=6.25x+225
D) y=-6.25+225​

Answers

The correct answer is letter B

HELPPP ASAP!! 10TH GRADE GEO

Answers

Answer:

[tex]\huge\purple {\boxed {m\angle FEG =23\degree}} [/tex]

[tex] \huge \orange {\boxed {m\angle FEH=113\degree}} [/tex]

Step-by-step explanation:

In the given circle, [tex] \overline{EG} [/tex] is diameter and [tex] \overline{EH} [/tex] is tangent at point E.

[tex]\therefore \widehat {EFG} [/tex] is a semicircular arc.

Since, measure of semicircular arc is 180°

[tex]\therefore m(\widehat {EFG})=180\degree... (1)[/tex]

[tex]\because m( \widehat {EF}) +m(\widehat {FG}) = m(\widehat {EFG}) [/tex] .... (2)

From equations (1) & (2)

[tex]\therefore 134\degree +m(\widehat {FG}) = 180\degree[/tex]

[tex]\therefore m(\widehat {FG}) = 180\degree-134\degree [/tex]

[tex]\therefore m(\widehat {FG}) = 46\degree [/tex]

By inscribed angle theorem:

[tex] m\angle FEG =\frac{1}{2} m(\widehat {FG} ) [/tex]

[tex] m\angle FEG =\frac{1}{2} \times 46\degree [/tex]

[tex]\huge\purple {\boxed {m\angle FEG =23\degree}} [/tex]

By tangent secant theorem:

[tex] m\angle FEH=\frac{1}{2} (46\degree +180\degree) [/tex]

[tex] m\angle FEH=\frac{1}{2} (226\degree) [/tex]

[tex] \huge \orange {\boxed {m\angle FEH=113\degree}} [/tex]

Other Questions
Which statements correctly describe and provide evidence for the double replacement reaction? What are the 4 threat indicators? What impact did the Ottoman Empire have on Eastern Europe? q1 sequential search 11 points q1.14 points grading comment: in what situation can we use sequential search? choice 1 of 5:when the array is sorted and the target is in the array. choice 2 of 5:when the array is sorted and the target is not in the array. choice 3 of 5:when the array is not sorted and the target is in the array. choice 4 of 5:when the array is not sorted and the target is not in the array choice 5 of 5:all of the above q1.22 points grading comment: what is the big o of sequential search? (n is the length of the array) choice 1 of 6:o(1) choice 2 of 6:o(log n) choice 3 of 6:o(n) choice 4 of 6:o(n log n) choice 5 of 6:o(n2) choice 6 of 6:o(!n) q1.35 points grading comment: using the array 11, 30, 34, 90, 99 as the input for sequential search, how many array elements are accessed in order to find the target element 34? choice 1 of 6:1 element choice 2 of 6:2 elements choice 3 of 6:3 elements choice 4 of 6:4 elements choice 5 of 6:5 elements choice 6 of 6:sequential search does not work here q2 binary search 9 points q2.13 points grading comment: in what situation can we use binary search? choice 1 of 6:when the array is sorted and the target is in the array choice 2 of 6:when the array is sorted and the target is not in the array choice 3 of 6:when the array is not sorted and the target is in the array choice 4 of 6:when the array is not sorted and the target is not in the array choice 5 of 6:1 and 2 choice 6 of 6:1 and 3 q2.22 points grading comment: what is the big o of binary search? 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(n is the length of the array) choice 1 of 6:o(log n) choice 2 of 6:o(n log n) choice 3 of 6:o(n) choice 4 of 6:o(n^2) choice 5 of 6:o(n^3) choice 6 of 6:o(!n) q3.23 points grading comment: what is the best case for selection sort? choice 1 of 4:when the array is already sorted choice 2 of 4:when the array is already sorted backward choice 3 of 4:when the array is sorted by pairs choice 4 of 4:there are no best case for selection sort q4 insertion sort 5 points q4.12 points grading comment: 4.1 (points) what is the big o of insertion sort? 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