I need Help with this problem

Answer Before defining the inverse of a function we need to have the right mental image of function.

Consider the function f(x) = 2x + 1. We know how to evaluate f at 3, f(3) = 2*3 + 1 = 7. In this section it helps to think of f as transforming a 3 into a 7, and f transforms a 5 into an 11, etc.

Now that we think of f as "acting on" numbers and transforming them, we can define the inverse of f as the function that "undoes" what f did. In other words, the inverse of f needs to take 7 back to 3, and take -3 back to -2, etc.

Let g(x) = (x - 1)/2. Then g(7) = 3, g(-3) = -2, and g(11) = 5, so g seems to be undoing what f did, at least for these three values. To prove that g is the inverse of f we must show that this is true for any value of x in the domain of f. In other words, g must take f(x) back to x for all values of x in the domain of f. So, g(f(x)) = x must hold for all x in the domain of f. The way to check this condition is to see that the formula for g(f(x)) simplifies to x.

g(f(x)) = g(2x + 1) = (2x + 1 -1)/2 = 2x/2 = x.

This simplification shows that if we choose any number and let f act it, then applying g to the result recovers our original number. We also need to see that this process works in reverse, or that f also undoes what g does.

f(g(x)) = f((x - 1)/2) = 2(x - 1)/2 + 1 = x - 1 + 1 = x.

Letting f-1 denote the inverse of f, we have just shown that g = f-1.

Definition:

Let f and g be two functions. If

f(g(x)) = x and g(f(x)) = x,

then g is the inverse of f and f is the inverse of g.

Exercise 1:

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Finding Inverses

Example 1. First consider a simple example f(x) = 3x + 2.

The graph of f is a line with slope 3, so it passes the horizontal line test and does have an inverse.

There are two steps required to evaluate f at a number x. First we multiply x by 3, then we add 2.

Thinking of the inverse function as undoing what f did, we must undo these steps in reverse order.

The steps required to evaluate f-1 are to first undo the adding of 2 by subtracting 2. Then we undo multiplication by 3 by dividing by 3.

Therefore, f-1(x) = (x - 2)/3.

Steps for finding the inverse of a function f.

Replace f(x) by y in the equation describing the function.

Interchange x and y. In other words, replace every x by a y and vice versa.

Solve for y.

Replace y by f-1(x).

Example 2.  f(x) = 6 - x/2

Step 1 y = 6 - x/2.

Step 2 x = 6 - y/2.

Step 3 x = 6 - y/2.

y/2 = 6 - x.

y = 12 - 2x.

Step 4 f-1(x) = 12 - 2x.

Step 2 often confuses students. We could omit step 2, and solve for x instead of y, but then we would end up with a formula in y instead of x. The formula would be the same, but the variable would be different. To avoid this we simply interchange the roles of x and y before we solve.

Example 3.  f(x) = x3 + 2

This is the function we worked with in Exercise 1. From its graph (shown above) we see that it does have an inverse. (In fact, its inverse was given in Exercise 1.)

Step 1 y = x3 + 2.

Step 2 x = y3 + 2.

Step 3 x - 2 = y3.

(x - 2)^(1/3) = y.

Step 4 f-1(x) = (x - 2)^(1/3).

Exercise 3:

Graph f(x) = 1 - 2x3 to see that it does have an inverse. Find f-1(x). Answer

Step-by-step explanation:

pls brain list

Answer:

3 1/2

Step-by-step explanation:

Answer:

he would need 2 and 2/3 pounds of potatoes

Step-by-step explanation:

you would add 2/3 together 4 times.

2/3 + 2/3 + 2/3 + 2/3 = 2 and 2/3

so oscar would need 2 and 2/3 pounds of potatoes.

hope I could be of great assistance to you.

Answer:

-1/9(-27)=3

Step-by-step explanation:

that's my answer

Answer:

B

Step-by-step explanation:

Answer:

Read explanation

Step-by-step explanation:

If you get a normal ruler it will be one foot total. You add the bigger measurements twice because they're an inch. Then you add half of those measures. It will be numbered 1, 2, 3... so on . In other words, the longer lines are inches and the shorter ones are centimeters.

Answer:

So here's a step by step

1: Pick up your ruler.

2: Make sure the ruler is not broken or cracked.

3: Find the thing you want to measure.

4: Put the ruler against the object.

5: Make sure the 0 on the ruler is right on the side of what your measuring.

6: When all that is done find the 2 on the ruler that is 2 inches

7: Then find the 1/2 mark next to the 2 that is 2 1/2 inches.

Dont know why you needed this but here lol.

Step-by-step explanation:

           May I have brainiest please I'm leveling up!

                           </3 PureBeauty

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Because there are two angles and they both are Complementary(90 degrees)

We can do 4x + 7x = 90

11x = 90

x= 8.18 repeating

Answer:

system 4.

Step-by-step explanation:

3x+6y=9

multiply by 2

6x+12y=18   ....(1)

-2x+-4y=4

multiply by 3

-6x-12y=12   ...(2)

add (1) and (2)

0+0=30

which is impossible .It has no solutions.

Answer:4) 3x+6y=9-2x-4y=4

Step-by-step explanation:

I got the answer right

Answer:

5

Step-by-step explanation:

Equation: 7.5 + 1.5x = 15

Subtract 7.5 from both sides you get 1.5x = 7.5

Divide both sides by 1.5 you get 5.

He can buy a total of 5 sour straws.

Hope this helps :)

Answer:

volume is 17157.28 :)

Step-by-step explanation:

Answer:

Talk-It-Up is the best value

Step-by-step explanation:

TIU=$95/month

TIC=$35/month + $10/gigabyte

Data usage=8 gigabytes

TIC=$35+$10(8)=$35+$80=$115

TIU is cheaper

Frankie is comparing the monthly costs of two cellphone plans:

-Talk-It-Up is Cheaper

Let us assume:

TIU = Talk-It-Up.

TIC = Talk-is-Cheap

Given:

TIU=$95/month

TIC=$35/month + $10/gigabyte

Data usage=8 gigabytes

Since, 95 [tex]\ge[/tex]115.

TIU is cheaper.

Learn more about "comparing the monthly costs":

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Answer:

D. Hyperbola

Step-by-step explanation:

I put B but it was wrong

D is the right answer

The given equation is represent a ''Hyperbola''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ 9x² - 5x - 3y² - 2y + 4 = 0

Now, We know that;

The standard form of the equation is,

⇒ ax² + by² + 2gx + 2fy + 2hxy + c = 0

For Hyperbola, The condition is,

⇒ h² > ab

For Ellipse ,  The condition is,

⇒ h² < ab

Here, We have;

⇒ h = 0

⇒ a = 9

⇒ b = - 3

⇒ ab = 9 x - 3 = - 27

⇒ h = 0

Hence, We get;

⇒ 0 > - 27

⇒ h² > ab

Thus, This equation is represent a ''Hyperbola''.

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Answer:

Wouldn't it be 7448?

Step-by-step explanation:

I multiplied 19 x 28 x 14 and got 7448?

Answer:

1

Step-by-step explanation:

8 + 1 = 9/9

-      -      

9.      9

Answer:

A - 6 hours and 40 minutes

B - 12 hours

Step-by-step explanation:

Candle A - After 6 hours: the candle will be 1 inch tall, because 6 times 1.5 = 9. You need an extra 40 minutes for the candle to burn completely, because 10/1.5 = 6 and 2/3

Candle B - After 12 hours, the candle will be completely burned, because 6/.5 = 12.

Equation - Initial height/inches burned per hour = time it takes for cnadle to burn down completely

Step-by-step explanation:

Given

13 sin θ = 5

sin θ = 5/13 = p/h

p = 5 , h = 13 and b = ?

By using Pythagoras theorem

b = √ h² - p²

= √ 13² - 5²

= √144

b = 12

Now

tan θ

= p / b

= 5 / 12

Hope it will help :)

Answer:

12

Step-by-step explanation:

It does not say what the tax is so the answer would be 12. You just divide 2 by 24.

Answer:

12

Step-by-step explanation:

24 divided by 2 is 12 or 2 times 12 is 24

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Answer: 30

Step-by-step explanation:

A=a+b

2h=12+3

2·4=30

Answer: 24

Step-by-step explanation:

Answer:

7.7 yards & 14.04 gallons

Step-by-step explanation:

so theres 1.1 yards per meter which can be written out as

1.1 yds/1 meter

multiply that by 7 meters would get you 7.7 yards

same with the punch:

0.26 gallons/ 1 liter times 54 liters = 14.04 gallons

Answer:

It's a total increase by 27,65%

Step-by-step explanation:

1,11 × 1,15 = 1,2765

1,2765 = +27,65%

Answer:

A drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale). The scale is shown as the length in the drawing, then a colon (":"), then the matching length on the real thing.

Step-by-step explanation:

Answer:

Answer down below!

Step-by-step explanation:

A scale drawing is a drawing that is downsized. They are usually used to see how small to make a particular thing.

Answer:

0.25 is a decimal and 25/100 or 25% is the percentage for 2/8.

Step-by-step explanation:

The result is: 0.25 and 25% is 2/8 as a decimal and percent.

Here, we have,

given that,

the fraction is:  2/8

now, we have to write as a decimal and percent.

so, we get,

2/8

[ dividing both numerator and denominator by 2 ]

= 1/4

= 0.25

so, we get, 0.25 is a decimal.

now, we have,

0.25 = 25/100 = 25%

so, we have, 25/100 or 25% is the percentage for 2/8.

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Answer: slope=-7/9. 10-17/10-1=-7/9

Answer:

The price changed by 92.5 %

Step-by-step explanation:

The regular price of lawn mover = 200 dollars

The new selling price = 85 dollars

Change in selling price = 200 -85 dollars = 115 dollars

% change == [tex]\frac{185}{200} * 100 = 92.5[/tex]

The price changed by 92.5 %

Answer:

54 republicans

50 democrats

Step-by-step explanation:

x=republicans

y=democrats

x+y=104

x=y+4

substitute for y

y+4+y=104

simplify

2y=100

y=50

x=54

Answer: 360 in. squared

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I did it and got it right