Consider the function f(x)=√2x−6. If f−1(x) is the inverse function of f(x), find f−1(−4).


Answers

Answer 1
Final answer:

To find the inverse function f−1(x) for f(x)=√(2x−6), we first express f(x) as y, swap x and y, remove the square root by squaring both sides, solve for y, and substitute -4 into the new expression. This calculation reveals that f−1(-4) is 11.

Explanation:

To find the value of f−1(-4) for the function f(x)=√(2x−6), we need to find the value of x such that f(x) equals -4. Here is how to find the inverse function:

First, replace f(x) with y: y = √(2x−6).Next, swap x and y to begin finding the inverse: x = √(2y−6).Square both sides to eliminate the square root: x² = 2y − 6.Rearrange the equation to solve for y: 2y = x² + 6.Divide both sides by 2: y = (x² + 6)/2.This new y is actually f−1(x), the inverse function.

To find f−1(-4), substitute -4 into the inverse function:

y = ((-4)² + 6)/2

y = (16 + 6)/2

y = 22/2

y = 11

Therefore, f−1(-4) = 11.

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Answer 2

To find f−1(−4) for the function f(x) = √(2x − 6), solve for x in terms of y, square both sides, solve for x, and then substitute the value to find that f−1(−4) equals 11.

To find the value of f−1(−4) for the function f(x) = √(2x − 6), follow these steps:

Solve for x in terms of y by setting y = f(x):
y = √(2x − 6)

Square both sides to eliminate the square root:
y2 = 2x − 6

Solve for x:
x = (y2 + 6) / 2

Replace y with x to get f−1(x):
f−1(x) = (x2 + 6) / 2

Now, find f−1(−4):
f−1(−4) = (−42 + 6) / 2 = (16 + 6) / 2 = 22 / 2 = 11

Thus, the value of f−1(−4) is 11.


Related Questions

What is 7 3/8 + 3 1/4?

Answers

Answer:

10 5/8

Step-by-step explanation:

1/4 = 2/ 8

7 3/8 + 3 1/4 = 7 3/8 + 3 2/8

7 3/8 + 3 2/8 = 10 5/8

Answer:

10.675

Step-by-step explanation:

An apartment complex has a total of 175 units. Of these, 154 units are occupied. What percent of the apartment are unoccupied?

Answers

Answer:

12%

Step-by-step explanation:

There are a total of 175 units in an apartment complex.

Out of which, 154 units are occupied.

Now, we have to find the percentage of the apartment which are unoccupied.

So, the number of units that are not occupied is (175 - 154) = 21.

Hence, the percentage of the number of unoccupied units of the apartment complex will be [tex]\frac{21}{175}\times 100 \% = 12 \%[/tex] (Answer)

Mary has 15 points with the total value of $1.75 if the coins are nickels and quarters how many of each kind are there

Answers

Answer:

The number of nickel coins is 10 and the number of quarter coins is 5

Step-by-step explanation:

The correct question is

Mary has 15 coins with the total value of $1.75 if the coins are nickels and quarters how many of each kind are there

Let

x ----> the number of nickel coins

y ----> the number of quarter coins

Remember that

[tex]1\ nickel=\$0.05[/tex]

[tex]1\ quarter=\$0.25[/tex]

we know that

Mary has 15 coins

so

[tex]x+y=15[/tex] -----> equation A

The total value of the coins is $1.75

so

[tex]0.05x+0.25y=1.75[/tex] ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (10,5)

therefore

The number of nickel coins is 10 and the number of quarter coins is 5

there are 45 green cars and bkack cars. the green cars are 27 more than the black. how many are green cars?

Answers

Answer:

18

Step-by-step explanation:

45-27=18

Answer:

18

Step-by-step explanation:

subtract 45 and 27 it gives u 18

On a scale drawing the scale is 1/2 inch=1 foot what are the dimensions on the scale drawing for a room that is 22 feet by 17 feet

Answers

Hey there! I'm happy to help!

We have a room that is 22 by 17 feet. We know that for every foot, we draw a 1/2 inch. This means that we need multiply our dimensions by 1/2 to find the dimensions of the drawing.

22×1/2=11

17×1/2=8.5

Therefore, the dimensions of the room are 11 feet by 8.5 inches. These are the dimensions of a normal white paper!

Have a wonderful day! :D

To convert the actual room dimensions of 22 feet by 17 feet to a scale drawing with a scale of 1/2 inch equals 1 foot, the length becomes 11 inches, and the width becomes 8.5 inches in the drawing.

When creating a scale drawing, the dimensions of the actual room need to be converted into scale dimensions. According to the scale given, which is 1/2 inch equals 1 foot, the actual room dimensions of 22 feet by 17 feet should be converted using this scale ratio.

To do this conversion, each actual dimension must be divided by the scale factor. The scale factor is determined by the number of feet that are represented by 1/2 inch. Since 1/2 inch is equivalent to 1 foot, the scale factor is 1 foot per 1/2 inch. Therefore, we calculate the dimensions as follows:

Length: 22 feet / 1 foot per 1/2 inch = 22 x 1/2 inches = 11 inches

Width: 17 feet / 1 foot per 1/2 inch = 17 x 1/2 inches = 8.5 inches

Thus, the dimensions on the scale drawing for a room that is 22 feet by 17 feet would be 11 inches by 8.5 inches.

How many times does 5 go into 236

Answers

Answer:

47.2

Step-by-step explanation:

236/5

47.5

Answer:

47.2

Step-by-step explanation:

Because,

= 236/5

= 47.2

Therefore, 47.2 tines 5 goes into 236.

erin makes $18 an hour. she works 40 hours a week. she found an apartment for $1,000 a month. Should erin rent the apartment?​

Answers

Answer:

Based on her monthly income YES

Step-by-step explanation:

18 × 4 = $720 a week and 720 × 4 = $2,880 a month

The rent for the apartment is $1,000 if Erin rent this place she will have an extra =1,880 for her living expenses after she pays for the rent so there would be no problem of her renting the place.

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
The student council at Princeton High School is making T-shirts to sell for a fundraiser, at a price of $11 apiece. The costs, meanwhile, are $9 per shirt, plus a setup fee of $140. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
Selling shirts will cover the $ in costs.

Answers

Final answer:

To cover costs, the student council needs to sell 70 T-shirts, which will cover the $770 in costs.

Explanation:

To solve the student council's problem, we need to find the number of T-shirts that must be sold so that the total revenue equals or exceeds the costs associated with making the T-shirts. Let's define x as the number of T-shirts to be sold. The total revenue from selling the T-shirts at $11 apiece can be represented as 11x. The costs consist of a setup fee of $140 and $9 per shirt, so the total cost is 9x + 140. To determine when the revenue will cover the costs, we can set up the following equation:

11x = 9x + 140

Solving this equation for x, we subtract 9x from both sides:

2x = 140

Then divide both sides by 2:

x = 70

Therefore, the student council needs to sell 70 T-shirts to cover their costs, which will be $770 ($11 per shirt multiplied by 70 shirts).

Two joggers run 8 miles north and 5 miles west . what is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point ?

Answers

Answer:9.4 miles

Hope this helps

Tia owns a fruit shop and is selling a fresh lot of apples and oranges. She wants the ratio of apples to oranges sold to be 4 to 2. Tia
wants to sell a total of 54 apples and oranges. How many apples should she sell?
A.
52 apples
B. 36 apples
C. 9 apples
D. 32 apples

Answers

Answer:

[tex]\large \boxed{\text{B. 36 apples}}[/tex]

Step-by-step explanation:

Let a = the number of apples

and o = the number of oranges

You have two conditions:

[tex]\begin{array}{lrcl}(1) & \dfrac{a}{o} & = & \dfrac{4}{2} \\\\(2) & a+ o & = & 54\\\end{array}[/tex]

Solve the equations for a

[tex]\begin{array}{rcll}2a & = & 4o & \text{Multiplied each side of (1) by 2o}\\\(3) \,2a - 4o& = & 0 &\text{Subtracted 4o from each side}\\a + o & = & 54& \text{This is equation (2)}\\(4) \, 4a +4o& = &216&\text{Multiplied each side by 4} \\6a& = &216&\text{Added (3) and (4)} \\a & = &\mathbf{36}&\text{Divided each side by 6} \\\end{array}\\\text{Tia should sell $\large \boxed{\textbf{36 apples}}$}[/tex]

Solve: 6x = -24 and x/7 = 3

Answers

Answer:

1) x = -4

2) x = 21

Step-by-step explanation:

6x = -24

6/6x=-24/6

x=-4

and

x/7 = 3

x/7*7=3*7

x=21

if the interior angle ofa regular polygon is 162° how many sides does it have

Answers

Answer:

20 sides.

Step-by-step explanation:

The exterior angle = 180 - 162 = 18 degrees.

Since the sum of the exterior angles = 360 degrees the number of sides

= 360 / 18

= 20 sides.

if I know A B C equals d e f can you stay B C equals ef​

Answers

If ABC and DEF are triangles, then yes you can!

How is the Distributive Property used to simplify operations with scientific notation

Answers

Answer:

See explanation

Step-by-step explanation:

Let a,b, and c be real numbers.

The distributive property says that:

[tex]a(b + c) = ab + ac[/tex]

Assuming we want to simplify:

[tex]10(5*10^{-1}+150*10^{-3})[/tex]

We apply the distributive property to get:

[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10+150*10^{-3} \times 10[/tex]

We can now use rules of exponents to simplify further:

[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10^{1} +150*10^{-3} \times 10^{1} [/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1 + 1} +150*10^{-3 + 1}[/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{0} +150*10^{-2}[/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2}x {10}^{2} [/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2 + 2}[/tex]

[tex]10(5*10^{-1}+150*10^{-3}) = 5+1.50*10^{0} = 6.5 \times {10}^{0} [/tex]

What numbers are divisible by 2 and 5 but not 3

Answers

Answer:

10  20 40

Step-by-step explanation:

2 Kate biked 9 miles north to the park, then 4
miles west to the mall. How far is Kate
from her starting point?

Answers

Cousin dididoosjaidjbbrjeikwjajkq
The answer to your question is 26 because 1 Kate is 13miles and you multiply the 13 to 2 then the answer is 26.

Each pair of polygons is similar. Find the values of x and y

Answers

x = 14 and y = 10

Explanation:

Two shapes are similar if they have the same form but not necessarily the same size. In other words, when shapes are similar they are in proportion. Since you haven't provided any diagram, I'll choose two irregular polygon that are similar as indicated in the figure below. So we can calculate both x and y with proportions as follows:

[tex]For \ x: \\ \\ \frac{x}{7}=\frac{16}{8} \\ \\ x=\frac{7\times 16}{8} \\ \\ x=14 \\ \\ \\ For \ y: \\ \\ \frac{y}{20}=\frac{8}{16} \\ \\ y=\frac{8\times 20}{16} \\ \\ y=10[/tex]

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The minor arc measures of circle Z are shown in the figure.
Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.
Use the drop-down menus to complete each statement.

Answers

Answer:

Part 1) Option a. TZY

Part 2) Option c. YZX

Step-by-step explanation:

The question is as following and see the attached figure

The minor arc measures of circle Z are shown in the figure.

Use the drop-down menus to complete each statement.

1) Angle UZT is congruent to angle _____

2) Angle VZW is congruent to angle____

Answer choices

1) a. TZY, b. XZW, c. VZW

2) a. UZV, b. TZY, c. YZX

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

Solution:

Part 1) Angle UZT is congruent to angle______

From the attached figure, we can deduce that:

∠UZT = 54°

∠TZY = 54°

So,

∠TZY = ∠UZT ⇒ both angles are congruent.

1. Angle UZT is congruent to angle TZY

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

Part 2) Angle VZW is congruent to angle_____

From the attached figure, we can deduce that:

∠VZW = 71°

∠YZX = 71°

So,

∠YZX = ∠VZW ⇒ both angles are congruent

2. Angle VZW is congruent to angle YZX

Answer: correct answer is TZY for first one and YZX for second

Step-by-step explanation:

Just chose those and got it correct :)

perimeter of a triangle formula

Answers

all you have to do is just add up all the sides to find the perimeter

Side 1 + side 2 + side 3 = perimeter

Step-by-step explanation:

You add all three side lengths

Please answer number 1

Answers

Step-by-step explanation:

[tex] \triangle \: ABC \cong \triangle \: FED[/tex]

Here, all the sides or angles of triangle ABC are congruent to the corresponding sides or angles of triangle FED. As both triangles are reflections of each other.

I am interested in a new van that costs $32,500. The salesman says he will give it to me for $27,950. What is the percent discount he is giving me?

Answers

Answer:

The salesman is giving you a 14% discount

Step-by-step explanation:

Do 27950/32500 to get 0.86

Then do 1-0.86=0.14

Multiply by 100 to get 14%

Hope this helped!

14% would be the percent discount given to you

Twenty-four hundredth in decimal notation

Answers

Answer:

  0.24

Step-by-step explanation:

Twenty-four hundredths = 24/100 = 24×(1/100) = 24×0.01 = 0.24

_____

Both 24/100 and 0.24 are pronounced "twenty-four hundredths."

Answer:

0.24

Step-by-step explanation:

If you say hundredths with ths it means that the number is at the right side the decimal point. so that means twenty four hundredths is at the right side of the decimal point so the answer will be 0.24 hundredths.

Two people bought a 13-inch sandwich to share. How many inches of sandwich does each person get if they split it evenly? Choose the correct answer from the choices below.

Answers

Answer:

6.5

Step-by-step explanation:

13/2 = 6.5 inches or 6 1/2 inches

Answer:

6 2/4ths

Step-by-step explanation:

Evaluate the function. F(x)=3/x-1/. F(-3)

Answers

f(-3)=3/(-3)-1 || f(-3)=3/3 || f(-3)=1

VERY VERY VERY VERY VERY URGENT!!?!!???


These triangles are similar.
True
False

Answers

Answer:

True

Step-by-step explanation:

There are 180 calories in 3 scoops of vanilla ice cream. How many calories are in 7 scoops.

Answers

Answer:

420 calories

Step-by-step explanation:

180 / 3 = 60 calories

60 x 7 =420 calories

Population in Millions
World: 7,691
Canada: 37.4
What percent of the 2019 world population lives in Canada? Round the percentage to three decimal places.

Answers

Answer:

0.486% of world population lives in Canada.

Step-by-step explanation:

Given: World Population= 7691 million.

           Canada Population= 37.4 million.

Now, finding the percentage of world population lives in Canada.

[tex]Population\ percentage= \frac{Canada\ population}{World\ population} \times 100[/tex]

⇒ [tex]Population\ percentage= \frac{37.4}{7691} \times 100[/tex]

⇒ [tex]Population\ percentage= 0.00486\times 100[/tex]

∴ [tex]Population\ percentage= 0.486\%[/tex]

Hence, 0.486% of world population lives in Canada.

Mary took out a student loan for $15000 at 4% simple interest. How much interest will she pay in 10 years? suppose she paid it off in 8 years instead of 10 years. how much would she save in interest?

Answers

Answer:$1200

Step-by-step explanation:

A cylindrical jar's lid has a radius of 4 inches. If the volume is 351.68 in , approximately what is the height of the jar?

Answers

Answer:

7 inches

Step-by-step explanation:

The volume of a cylinder is calculated using

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

where r =4 inches is the radius and V=351.68 is the volume.

To find the height of the jar, we substitute these values and solve for h.

[tex]351.68 = 3.14 \times {4}^{2} \times h[/tex]

[tex]351.68 = 50.24h[/tex]

Divide both sides by 50.24 to get:

[tex]h = \frac{351.68}{50.24} [/tex]

h=7 inches

Therefore the height of the jar is 7 inches

Marco buys a certain brand of shampoo from a supplier at 7.25 dollars per bottle .He sells it at a markup of 25 percent. What is the markup .

Answers

Final answer:

Marco buys shampoo at $7.25 per bottle and sells it with a 25% markup, making the markup $1.81 per bottle. The selling price, therefore, is $9.06 per bottle.

Explanation:

The question is about calculating the markup applied by Marco on a bottle of shampoo. Marco buys the shampoo at $7.25 per bottle and sells it at a markup of 25 percent. The markup is calculated based on the cost price of the product. In this case, to find the markup amount, we use the formula: Markup = Cost Price * Markup Percentage. So, the markup on each bottle of shampoo is $7.25 * 0.25 = $1.81. Therefore, Marco applies a $1.81 markup on each bottle of shampoo.

To determine the selling price, one can add the markup to the cost price, which would be $7.25 + $1.81 = $9.06. This is Marco's selling price per bottle after applying the 25 percent markup.

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