I NEED HELP WITH QUESTION PLEASE!!
What is the inverse of f(x)
(x) = (x-4)² for x ≥ 4?

I NEED HELP WITH QUESTION PLEASE!!What Is The Inverse Of F(x)(x) = (x-4) For X 4?

Answers

Answer 1

Answer:

4th choice [tex]\bold{f^{-1}(x) = \sqrt{x} + 4}[/tex]

Step-by-step explanation:

Definition of the inverse of a function

A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing. We can write this in terms of the composition of f and g as g(f(x))=x. The domain of f becomes the range of g and the range of f becomes the domain of g

To solve for the inverse of the function [tex]f(x) =\left(x-4\right)^2[/tex]

Let [tex]y=\left(x-4\right)^2[/tex]

[tex]\mathrm{Replace}\:x\:\mathrm{with}\:y[/tex] [tex]\text{ and replace }\:y\:\mathrm{with}\:x[/tex]

[tex]x=\left(y-4\right)^2[/tex]

Switch sides
[tex]\left(y-4\right)^2=x[/tex]

Take square roots on both sides
[tex]y-4=\pm\sqrt{x}[/tex]

Add 4 on both sides to solve for y

[tex]y = \pm\sqrt{x} + 4[/tex]

We have two solutions

[tex]y=\sqrt{x}+4,\:y=-\sqrt{x}+4[/tex]

To determine which one of these to be chosen not that in the given choices we can eliminate the first two since x cannot be negative

The third choice can also be eliminated since
[tex]-\sqrt{x} + 4[/tex] is a decreasing function for [tex]x \ge 0[/tex]

So the last answer choice is correct and the inverse of[tex]f(x) = (x-4)^2[/tex]

is given by [tex]f^{-1}(x) = \sqrt{x} + 4[/tex]

Answer:4th choice [tex]\bold{f^{-1}(x) = \sqrt{x} + 4}[/tex]

Note

Domain of (x-4)² is [4, ∞) since x ≥ 4 and (x-4)² cannot be negative

Range of (x-4)² is [0, ∞)

Domain of [tex]\sqrt{x}\:+\:4[/tex] is [0, ∞)

Range of [tex]\sqrt{x}\:+\:4[/tex] is [4, ∞)

so indeed the domain of (x-4)² has become the range of [tex]\sqrt{x}\:+\:4[/tex] and the range of (x-4)² has become the domain of [tex]\sqrt{x}\:+\:4[/tex]

Related Questions

Is 7.65 greater or less than 7.7

Answers

Answer:

less than

Step-by-step explanation:

Factor out the greatest common factor.
3x³-18x² + 12x

Answers

Answer:

x² - 6x + 4

Step-by-step explanation:

Hello!

Factor each term completely:

3x³ = (3)(x)(x)(x)-18x² = (-1)(2)(3)(3)(x)(x)12x = (2)(2)(3)(x)

Common factors that are shown in all 3 terms are x and 3.

Divide each term by 3x:

(3)(x)(x)(x) ÷ 3x = (x)(x) = x²(-1)(2)(3)(3)(x)(x) ÷ 3x = (-1)(2)(3)(x) = -6x(2)(2)(3)(x) ÷ 3x = (2)(2) = 4

Combine the terms: x² - 6x + 4

what is the solution to -3/8x-11=4

Answers

Answer: -40

Step-by-step explanation:

Answer:

-1/40

Step-by-step explanation:

-3/8x -11+11=4+11

-3/8x=15

-3/8x x=15x

-3/8=15x

15x/15= -3/8/15

x=-1/40

Hope this helps!^^

identify the coefficient, constant, and variable in the expression: - 5 + 8w

Answers

Answer:

coefficient=8

constant=-5

variable=x

Step-by-step explanation:

Answer:

-5 constant

8 coefficient

w variable

Step-by-step explanation:

On Monday, Saffron bakes
324 pastries in the morning and some more in the
afternoon. She sells 584 pastries. At the end of the
day she has 52 pastries left. How many pastries did
she bake in the afternoon?

Answers

the number of pastries that she bake in the afternoon is equal to 312 pastries.

We are given that:

Saffron sells 584 pastries in the whole day and 52 pastries are left at the end of the day.

Now, we will use addition to find the total number of pastries that is being made in the day.

Total pastries = 584 + 52

Total pastries = 636

Now, she bake 324 pastries in the morning.

So, the number of pastries baked in the afternoon = 636 - 324

In afternoon = 312.

Therefore, we get that the number of pastries that she bake in the afternoon is equal to 312 pastries.

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greg sets his watch for the correct time exactly one week later he finds that his watch 1 1 over 3 minutes it loses time at the same rate for eight weeks write a multiplication expression that describes the sittuation find the product and explain how it is related to the problem?

Answers

The product or overall change in time for 8 weeks will be 29.33 minutes.

What is a statement?

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

After one week, Greg's watch has lost 11/3 minutes. If the watch continues to lose time at the same rate, we can say that the change in time is 11/3 minutes per week.

According to given question we have

(11/3 minutes/week) x (8 weeks) = 29.33 minutes

Therefore, the product or overall change in time for 8 weeks will be 29.33 minutes.

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What is the equation 5y+22=5x-33 written in slope intercept form

Answers

Answer:

y = x - 11

Step-by-step explanation:

5y + 22 = 5x - 33

5y = 5x - 33 - 22

5y = 5x - 55

y = x - 11

Which expression shows the first step in dividing 5x + 3 by x?

Answers

The First step Linear Expression shows is 5+3/x

An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1. As an illustration, while x is a variable raised to the first power, x2 is a variable raised to the second power. An illustration of a constant is 5.

so when this linear expression 5x + 3 is divided by x then the first step will be

5 + 3/x

Answers

Answer:

Step-by-step explanation:

233% = 2.33

2 2/3 = 2.6

All work and the answer is provided in the screenshot that is attached! :)

Have a great day!

Solve
4x + 8y = 16 for X.

Solve for x

Answers

Answer:

x = 4 - 2y

Step-by-step explanation:

4x + 8y = 16

or, x + 2y = 4

or, x = 4 - 2y

Answer:4-2y

Step-by-step explanation:

If an arrow is shot upward on the moon with a velocity of 58 m/s, its height in meters after t seconds is given by y=58t−.83t2.

(a) Find the average velocity over the given time intervals:
(1) [1,1.5]
(2) [1,1.1]
(3) [1,1.01]
(4) [1,1.001]

(b) Find the instantaneous velocity after one second (to the nearest hundredth).

(1) m/s
(2) m/s
(3) m/s
(4) m/s
(b) m/s

Answers

The 58 m/s initial velocity of the arrow with height, y = 58•t - 0.83•t², gives;

(1) 55.925 m/s

(2) 56.257 m/s

(3) 56.3317 m/s

(4) 56.33917 m/s

(b) 56.34 m/s

How can the average and instantaneous velocity be calculated?

Initial velocity of the arrow = 58 m/s

Height of the arrow is; y = 58•t - 0.83•t²

The above kinematic equation can be analyzed as follows;

(1) The height at t = 1 is found as follows;

y = 58 × 1 - 0.83 × 1² = 57.17

Height at t = 1.5 s. is y = 58×1.5 - 0.83×1.5² = 85.1325

Average velocity = ∆y/∆t

Which gives;

Average velocity = (85.1325-57.17)/(1.5-1) = 55.925

The average velocity in the interval [1, 1.5] is therefore;

55.925 m/s

(2) [1, 1.1]

Height at t = 1.1 s. is y = 58×1.1 - 0.83×1.1² = 62.7957

Which gives;

Average velocity = (62.7957-57.17)/(1.1-1) = 56.257

The average velocity is 56.257 m/s

(3) [1, 1.01]

Height at t = 1.01 s. is y = 58×1.01 - 0.83×1.01² = 57.733317

Which gives;

Average velocity = (57.733317-57.17)/(1.01-1) = 56.3317

The average velocity is 56.33 m/s

(4) [1, 1.001]

Height at t = 1.01 s. is y = 58×1.001 - 0.83×1.001² = 57.22633917

Which gives;

Average velocity = (57.22633917-57.17)/(1.001-1) = 56.33917

The average velocity is 56.33917 m/s

(b) The equation for the instantaneous velocity is found as follows;

v = dy/dt = 58 - 2×0.83•t

After 1 second, we have;

t = 1

v = 58 - 2×0.83 × 1 = 56.34

The instantaneous velocity at t = 1 seconds is 56.34 m/s

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Can someone help me get the points I’ll make u brilliant the points are S T R U

Answers

Using translation concepts, the coordinates of the vertices after a rotation 180º clockwise around the origin is:

S': (-4,-10), R'(-4,-3), U'(-8,-3) and T'(-8,-10).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the coordinates (x,y) of the vertices are given as follows:

S(4,10), R(4,3), U(8,3), T(8,10).

The rule for a rotation 180º clockwise around the origin is:

(x,y) -> (-x,-y).

Hence the vertices of the rotated image will be given as follows, applying the above rule:

S': (-4,-10), R'(-4,-3), U'(-8,-3) and T'(-8,-10).

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1/3 divided by 3/5 = 1/3 divided by M. What is M. I came up with 3/5

Answers

Answer:

Yes you are correct

Step-by-step explanation:

1/3 / 3/5 = 1/3 / M

3*1/3 / 5*3/5 = 3*1/3 / 5M

3/3 / 15/5 = 3/3 / 5M

1/3=1/(5M)

5M * 1/3 = 1

5M * 3 * 1/3 = 1 * 3

5M=3

M=3/5 √

Can somebody please help me I'm trying to find out what 2 + 2 is

Answers

Answer:

2+2 = 4

Step-by-step explanation:

Let's visualize this using # signs

we have two groups of two # signs, so let's map that out

If you count the individual # signs, it is 4. You can also use this model to figure out 2 *2 (4)

I hope this helps :)

Answer:

Step-by-step explanation:

2+2

2+1+1

3+1

Robert made 3 more than twice as many baskets as Billy did in the
basketball game.

Answers

The algebraic expressions of the statements are x = 6y - 4 and r = 3 + 2b

How to determine the statement as an algebraic expression?

Statement 1

The statement is given as

Ramona has 4 less than 6 times as many one dollar bills as Rita has

Let the number of one dollar bills owned by Ramona be x and the number of one dollar bills made by Rita be y

So, the interpretation of the statement is

x = 6y - 4

Hence, the algebraic expression of the statement is x = 6y - 4

Statement 2

The statement is given as

Robert made 3 more than twice as many baskets as Billy did in the basketball game.

Let the number of baskets made by Robert be r and the number of baskets made by billy be b

So, the interpretation of the statement is

r = 3 + 2b

Hence, the algebraic expression of the statement is r = 3 + 2b

Answers

The function P(x) for the total profit from the production and sale of x toilets is P(x) = 90x - 16600

How to formulate a function P(x) for the total profit from the production and sale of x toilets?

The given parameters are

Fixed cost = 16600

Variable cost = 67 per toilet

Cost of toilet = 157 per toilet

Let the number of toilets be x

So, the cost function is

C(x) = Fixed cost + Variable cost * Number of toilets

This gives

C(x) = 16600 + 67x

Also, we have the revenue function to be

R(x) = Cost of toilet * Number of toilets

This gives

R(x) = 157x

The function P(x) for the total profit from the production and sale of x toilets is

P(x) = R(x) - C(x)

So, we have

P(x) = 157x - 16600 - 67x

Evaluate

P(x) = 90x - 16600

Hence, the function P(x) for the total profit from the production and sale of x toilets is P(x) = 90x - 16600

Answers

0.166 is the standard form of that

What are the next two terms in the following sequence? 6, 3, 12, 6, 24.....

Answers

Answer:

12, 48

The pattern is: Divide by 2, then multiply by 4

is this proportion or not a meal delivery service cost $10 to sign up ,plus $24.99 each month ASAP

Answers

Answer:

This is not proportional.

Step-by-step explanation:

If there was no meal delivery cost than it would be proportional.

NEED ANSWERS ASAP WE NEED IT TOMORROW GRADE SIX MATH

1.What is the difference when ⅓ is subtracted from ¾?

2.The sum of ³/⁷ and ½ is equal to? ___

3.The difference between ⅘ and ¼ is ___

4. The sum of 2¼ and 1³/²⁴ subtracted by 1¾ is ______

Answers

The fractions are what is different

HELP ME OUT PLEASE!!!!!!!!

Answers

Answer:

-3

Step-by-step explanation:

Answer:

x-intercepts: (6,0)

y-intercepts: (0,3)

4. Old Faithful, Yellowstone National Park's most famous
geyser, shoots a spray of steam and hot water 50 m
into the air. Is this height greater or less than 5,000 mm?

Answers

Greater because a meter is greater than a millimeter.

Also can I get the brainliest pls?

select two points that lie on the same line throught (0,0), then select an equation that describes the relationship between the coordinates x and y

Answers

Two collinear points on a line are given in the table below:

x, y

0 0 (0,0)

2 1 (2,1)

Select the points that lie on the line. and the relationship between the coordinates x and y.

(4,2)

(4, 3)

(7,2)

4/8, 2/8

Answer:

(4,2) and ([tex]\frac{4}{8}[/tex],[tex]\frac{2}{8}[/tex]) are lie on the line, and y = [tex]\frac{1}{2}[/tex] x , is showing the relationship of x and y coordinates of given line.

Given that

The co-ordinates of line is (0,0) and (2,1).

To find

The points that lie on the line, and The relationship between the coordinates x and y.

So, according to the question

We have,

The X and Y co-ordinates of line (0,0) and (2,1).

For finding any point that lie on line, first we have to find the slope of given line,

So, we know that

slope (m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where,

x₁ = 0 and x₂ = 2

y₁ = 0 and y₂ = 1

Now, putting the values, we will get

(m) = [tex]\frac{1-0}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

m = [tex]\frac{1}{2}[/tex]

We know that, the equation of line

y-y₁ = m(x- x₁ )

y-0 = [tex]\frac{1}{2}[/tex] (x- 0)