The graph of any function and the graph of its inverse are symmetric with respect to the

The Graph Of Any Function And The Graph Of Its Inverse Are Symmetric With Respect To The

Answers

Answer 1

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

A function should be one - to - one and onto in order to have inverse.

and to find the point on its inverse function we swap the value of x - coordinate and y - coordinate.

like (x , y) becomes (y , x)

The only way we get (y , x) is by taking image of point (x , y) about line : y = x

[tex] \qquad \large \sf {Conclusion} : [/tex]

we can conclude that the graph of a function and it's inverse is symmetric about equation (line) : y = x


Related Questions

A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Kelvin has enough money to buy only 19 sweets. What is the biggest number of sweets that he can get from the shop?

Answers

Answer:

Kelvin can get 6 free sweets

Write down the equation for the following
i,Grade 7 students received a total of 88 books from world vision.they received 63 books on Monday and g books on Tuesday

ii,Solve the equation above​

Answers

Grade 7 got total 88 books
No. Of books given on Friday = 63
No. Of books on Tuesday =g
g = 88 - 63
g = 25

Everyone in Sandy's class has to do a science project. Out of 50 students, 56% have completed their projects.
How many students still need to do their projects?

Pls help ASAP

Answers

Answer:

22

Step-by-step explanation:

100 - 56 is 44.  44% have still not done the project

.44 x 50 = 22

Answer:

22 coz 56% of 50 which is the total is 28. Then the remaining 44%is22

Step-by-step explanation:

what is 2^c=8 (please help)

Answers

Answer:

c=3.

Step-by-step explanation:

∵2*2*2=8,

∴2^3=8.

∵2^c=8,

∴c=3.

If two fair dice are rolled, what is the probability that the total showing is either even or less than five?

Answers

The Probability that the total showing is either even or less than five = 5/6

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

According to the given data:

The example space for rolling two dice is:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

36 events total.

Events that have a sum that is even or less than Five .

Total instances when the aggregate is even or less than Five equals 30.

P(sum is even or less than 5)

= (Total no of favorable event)/(Total no of event)

= 30/36

=5/6

probability that the total showing is either even or less than five = 5/6

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The school puts up fencing around an area in the shape of a hexagon for an outdoor concert. how much fencing does the school use? round your answer to the nearest whole yard.

Answers

The total length of school installs fencing around a hexagon-shaped area for an outside concert, is 36 yards.

What is the distance formula?Distance is a numerical measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other criteria in physics or common usage. The distance between two points A and B is commonly expressed as |AB|.

To find the fencing used by the school:

The distance formula can be given as: [tex]d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1})^{2} }[/tex]

First, we must calculate the length of the hexagon using the distance formula.

The hexagon's coordinates, according to the graph, are:

(-5, 4), (0, 6), (5, 4), (6, -2), (0, -4), and (-6, -2)

The distance between (-5, 4), (0, 6): [tex]d=\sqrt{(5)^{2} +(6-4)^{2} }[/tex]

d = √29 yards

Similarly, the distance between (-5, 4) and (6, -2):

= √37 yards

And the distance between (6, -2) and (0, -4):

= √40 yards

Amount of fencing required = 2(√29+√37+√40):

= 35.58 units ≈ 36 yards

Therefore, the total length of school installs fencing around a hexagon-shaped area for an outside concert, is 36 yards.

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The complete question is given below:

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

The school puts up fencing around an area in the shape of a hexagon for an outdoor concert. How much fencing does the school use? Round your answer to the nearest whole yard.

Answer:

36 yards of fencing

Step-by-step explanation:

the reason I know this is because I got it right.

What is the 7th term of an AP: 50+45+40

Answers

Answer:

20

Step-by-step explanation:

using the arithmetic progress formula

tn=a+(n-1)d

from the series given above a which is your first term is 50

the d which is the common difference.. you minus the first term from the second term which is 45-50=-5

so the 7th term which our n=7

we have:

t7=50+(7-1)(-5)

t7=50+(6)(-5)

t7=50-30

t7=20

Answer:

a₇ = 20

Step-by-step explanation:

the nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 50 and d = 45 - 50 = - 5 , then

a₇ = 50 + (6 × - 5) = 50 + (- 30) = 50 - 30 = 20

Two cars raced at a race track. the faster car traveled 20 mph faster than the slower car. in the time that the slower car traveled 165 miles, the faster car traveled 225 miles. if the speeds of the cars remained constant, how fast did the slower car travel during the race? distance (mi) rate (mph) time (h) slower car 165 r startfraction 165 over r endfraction faster car 225 r 20 startfraction 225 over r 20 endfraction 55 mph 60 mph 75 mph 130 mph

Answers

If the faster car is travelling 20 mph faster then slower car then the speed of slower car is 55mph and faster car is 75 mph.

Given that the faster car is travelling 20 mph faster than slower car and when slower car travels 165 miles the faster car travels 225 miles.

We are required to find the speed of slower car and faster car.

let the speed of slower car be x mph.

In this way the speed of faster car be (x+20) mph.

Speed=Distance/ time

We have to first take slower car.

x=165/Time

Time=165/x-----------1

Now by taking faster car.

x+20=225/time

Time=225/(x+20)-------2

From equation 1 an equation 2.

165/x=225/(x+20)

225x=165x+3300

225x-165x=3300

60x=3300

x=55 mph

Faster car=55+20

=75 mph.

Hence if the faster car is travelling 20 mph faster then slower car then the speed of slower car is 55mph and faster car is 75 mph.

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Which option is the fraction 28/31 closest to? 0, 1/2 or 1?

Answers

Answer:

1 is the closest to 28/31

Step-by-step explanation:

0 is technically 28 spaces away and 1/2 is around 13 spaces away but 1 is only 3. :)

The option that is closest to the fraction 28/31 is 1 because 28/31 is close to becoming 31/31- equivalent to one.

Use the graph to find the local minimum and the local maximum for the given function

Answers

The local minimum on the interval [-3, 0] is -16, the local maximum on the interval [0, 3] is 4 and the local minimum on the interval [0, 3] is -3

What is a local minimum?

In a function, a point located at the local minimum is a point that is at a lower coordinate compared to the other neighboring points

What is a local maximum?

In a function, a point located at the local maximum is a point that is at a higher coordinate compared to the other neighboring points

How to determine the local minimum and the local maximum?

The complete question is added as an attachment

In the first interval, [-3, 0], the lowest point in the interval is located at (-16, -1.5)

This means that the local minimum on the interval [-3, 0] is -16

In the second interval, [0, 3], the highest maximum in the interval is located at (4, 1)

This means that the local maximum on the interval [0, 3] is 4

In the second interval, [0, 3], the lowest minimum in the interval is located at (0, -3)

This means that the local minimum on the interval [0, 3] is -3

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Find the surface area of the figure.
8 in.
8 in.
12 in.
12 in.
8 in.
10 in.
SA = [? ]in.²
10 in. SA
Enter P
I

Answers

The surface area of the rectangular prism shown in the figure is 512 in²

What is an equation?

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Surface area = 2(8 * 8) + 2(12 * 8) + 2(8 * 12) = 512 in²

The surface area of the rectangular prism shown in the figure is 512 in²

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What is the range of this function? (negative infinity, infinity) left-bracket negative 1, infinity) (negative 1, infinity) (0, infinity)

Answers

The range of the function [tex]f(x) = -2(6)^{x} +3[/tex] discovered using exponential function is ( -∞, 3).

What is the range?The difference between the greatest and smallest numbers is called the range.

What is an exponential function?

The following equations represent an exponential function: [tex]y=ab^{x} +c[/tex]

In which:

a is the initial value.b is the rate of change.c is the vertical shift.

As for the range, we have:

If a > 0, the range is (c,∞).If a < 0, the range is (-∞,c).

In this problem, the function is given by: [tex]f(x) = -2(6)^{x} +3[/tex]

The coefficients are a = -2 0, b = 6, and c = 3, and the range is  (-∞,3).

Therefore, the coefficients are a = -2 0, b = 6, and c = 3, and the range is  (-∞,3).

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The complete question is given below:

What is the range of the function f(x) = –2(6x) + 3? (negative infinity, negative 2 Right-bracket (negative infinity, 3) Left-bracket negative 2, infinity) Left-bracket 3, infinity)

Answer:B

Step-by-step explanation:edge lolololololololloll

A dealer bought digital watches at Rs 5,500 per piece and fixed the price of each watch to make 20% profit. How much should a customer pay for it with 13% VAT?​

Answers

Answer:

A dealer bought digital watches at Rs 5500  per piece and fixed the price of each watch to make 20  profit. How much should a customer pay for it with 13  VAT? A trader purchased a laptop for Rs 45000   and marked its price to make 24  profit.

Step-by-step explanation:

The base of each triangle varies inversely with the height. what are the possible base is 14 and height of a second triangle if the first triangle's base is 14 and its height 6 is ?

Answers

The possible base and height of a second triangle are:

B = 5 H = 12

What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

To find the base and height of the triangle:

First, we must find the constant of variation (k).

The problem indicates that the base of each triangle varies inversely with the height.

So, this can be represented as below:

B = k/H

B is the base of the triangle (B=10). H is the height of the triangle (H=6). k is the constant of variation.

When we clear "k", we obtain:

B = k/H k = BxH k = 10x6 k = 60

Now, we have:

B = 60/H

We can give any value to "H" and you will obtain the base of the second triangle.

If H = 12, then:

B = 60/H B = 60/12 B = 5

Therefore, the possible base and height of a second triangle are:

B = 5 H = 12

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QPS=
Help me please! Thankss

Answers

Answer:

44°

Step-by-step explanation:

[tex]\frac{134-46}{2}=44[/tex]

.

Help on this math problem!! if there is any work that can be shown it would be great thanks!!!

Answers

I’m just assuming this but I think it’s 64.4 because I think all of the subtraction are taken away by 38 so I just took 102.4-38

find the missing numbers in the following equal ratios:
[tex]\frac{?}{3} = \frac{?}{6} = \frac{8}{?} = \frac{16}{24}[/tex]

Answers

First blank: Dividing the numerator and denominator of 16/24 by 8 gives the unknown to be 2.

Second blank: Dividing the numerator and denominator of 16/24 by 4 gives the unknown to be 4.

Third blank: Dividing the numerator and denominator of 16/24 by 2 gives the unknown to be 12.

Select the correct answer. jackson is conducting an experiment for his physics class. he attaches a weight to the bottom of a metal spring. he then pulls the weight down so that it is a distance of 6 inches from its equilibrium position. jackson then releases the weight and finds that it takes 4 seconds for the spring to complete one oscillation. which function best models the position of the weight?

Answers

The function that best models the position of the weight is s(t) = 6cos (pi/2*t).

How to illustrate the function?

From the information, we know that the spring is going to have a sin or a cos equation.

We have that the maximum distance of the spring is 6 inches and it is achieved at t=0. We have that the function is of the form 6sin(at+B).

We have that the period is 4 minutes and therefore that the time component in the equation needs to make a period (2pi) in 4 minutes.

In general, a=2pi/T where a is this coefficient, T is the period. Finally, for B, since sin(pi/2)=1, we have that B=pi/2 because when t=0, we have that 6sin(B)=6.

Substituting, we have s(t) = 6cos (pi/2*t).

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Given: y varies directly with x and has a constant rate of change of 7. when the value of y is 12, then the value of x would be _____.

Answers

Answer:X=12/7

Step-by-step explanation:

Y [tex]\alpha[/tex] X

⇒Y=KX

Where K is the constant

From the question,k=7

⇒ When Y=12,

y=KX

12=7X

X=12/7

6. Encik Azmi bought a locally made car for RM55 000. After 6 years, Encik Azmi wishes to sell the car. Based on the explanation from the used car dealers, the price of Encik Azmi's car will be calculated using the formula RM55 000 (8)". In this situation, n is the number of years after the car is bought. What is the market value of Encik Azmi's car? State your answer correct to the nearest RM. RM55 000​

Answers

The result is 859,375,000.

What does multiplication mean?The result of two numbers being multiplied is known as the product. The multiplier is the number of such equal groups, and the multiplicand is the number of items in each group.Calculating the outcome of successive additions of two numbers is known as multiplication. The multiplication formula is 4 times 2 equals 8.Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests will be given in addition, subtraction, multiplication, and division. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.Multiplication has the following three characteristics: commutative, associative, and distributive.

The market value of Encik Azmi's car:

Get the answer by multiplication.

[tex]=55000*8^{6}[/tex]

=55000*15625

=859,375,000

The market value of Encik Azmi's car is 859,375,000.

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Find the equation of a line that passes through the points (-2,-3) and (4,1)

Answers

The equation of the line from give points is y = 2/3x - 5/3.

According to the statement

We have given that the two points which are (-2,-3) and (4,1)

And we have to find the equation of a line that passes through the given points.

So,For this purpose,

First, we need to determine the slope of the line. The slope can be found by using the formula:

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

Where

m is the slope and

Substituting the values from the points in the problem gives:

m = 1 + 3 /4 + 2

m = 4/6

m = 2/3.

And then

Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:

[tex]y - (y_1) = m(x -x_1)[/tex]

Put the values in it then

y - (-3) = 2/3 (x-(-2))

y +3 = 2/3 (x +2)

3y + 9 = 2x + 4

3y - 2x = 4 -9

3y -2x = -5

3y = 2x - 5

y = 2/3x - 5/3.

So, The equation of the line from give points is y = 2/3x - 5/3.

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The sum of 10 consecutive integersstarting with 11, equals the sum of 5 consecutive integers, starting with
(A) 22
(B) 29
(C) 31
(D) 33

Answers

Answer: [tex]\large\boxed{29}[/tex]

Step-by-step explanation:

The sum of 10 consecutive integersstarting with 11

= 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155

Lets try 29:

29 + 30 + 31 + 32 + 33 = 155

Therefore our answer is:

[tex]\large\boxed{29}[/tex]

Can I get some help finding the x of the triangle please?

Answers

Answer:

61

Step-by-step explanation:

You can see that the sides are both 6. That means that this triangle is an isosceles triangle.

Therefore do this:

180-58=122

122/2= 61

So x= 61 Degrees

Hope This helps! :)

Answer:

x = 61

Step-by-step explanation:

This triangle is an isosceles triangle which means 2 sides are congruent. This also means the 2 angles across from the congruent sides are congruent. So, you would subtract 58 from 180 which equals 122. Then you would divide that in half, which gets you 61. (The angle 58 is the one across from the side that is not congruent to the others. That is why I used it)

A plan for a baseball diamond is drawn in a coordinate plane. The baseball diamond is in the shape of a square with vertices at approximately (0, 64), (64, 0), (0, -64), and (-64, 0). One unit in the coordinate plane represents 1 ft. What is the approximate area of the baseball diamond?

Answers

The area of the baseball diamond is 8192 sq. units.

We assume the square-shaped, baseball diamond to be ABCD with A = (0, 64), B = (64, 0), C = (0, -64), and D = (-64, 0).

The side of the square can be computed using the distance formula,

D = √((x₂ - x₁)² + (y₂ - y₁)²), when the endpoints of a line are (x₁, y₁) and (x₂, y₂).

Thus, the side of the square,

a = √((x₂ - x₁)² + (y₂ - y₁)²),

or, a = √((64 - 0)² + (0 - 64)²) {Considering A(0,64) and B(64, 0) as the endpoints,

or, a = √(64² + (-64)²),

or, a = √(4096 + 4096),

or, a = 64√2 units.

Now, the area of the square can be calculated using the formula, A = a², where A is the area and a is the side of the square.

Thus, the area of the square = (64√2)² = 4096*2 = 8192 sq. units.

Thus, the area of the baseball diamond is 8192 sq. units.

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PLS HELP IS IT TRUE OR NOT

Answers

Answer:

True

Step-by-step explanation:

All faces of a cube are the same.

What is the solution to the equation
O x = -3
x = -3 and x=0
O x = 0 and x = 3
O x = 3
X+3
2 ?
2x²

Answers

The solution to the equation 1/x = x + 3/2x^2 is x  = 0 or x = 3

How to determine the solution to the equation?

The equation is given as:

1/x = x + 3/2x^2

Cross multiply in the above equation

2x^2 = x^2 + 3x

Evaluate the like terms

x^2 - 3x = 0

Factor out x

x(x - 3) = 0

Solve for x

x  = 0 or x = 3

Hence, the solution to the equation 1/x = x + 3/2x^2 is x  = 0 or x = 3

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Answer:

The Answer Is "x=3"

Step-by-step explanation:

I just did it

When the dollar price of pounds rises, for example, from $1 = 1 pound to $2 = 1 pound, the dollar has ______ relative to the pound.

Answers

The dollar gains depreciated relative to the pound when the price of pounds in dollars increases, for instance, from $1 = 1 pound to $2 = 1 pound.

What is Depreciated relative?

Devaluation of a currency can take place in both absolute and relative terms. When the value of one currency declines in relation to the values of other currencies, this is referred to as a relative devaluation. For instance, the British pound sterling may be worth more today than it did yesterday in terms of US dollars.

A currency's value declines when compared to other currencies, which is known as currency depreciation. Political unrest, interest rate differences, weak economic fundamentals, and investor risk aversion are a few examples of the causes of currency devaluation.

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What is the product of –3 and 5?

Answers

-15 is the answer you’re looking for. I’m pretty sure.

Select all of the values of x that are solutions to 17-7x> 3(10x-4) + 61.

-2
-4
-1
2
5
0

Answers

Answer: -2, -4, -1

Step-by-step explanation:

[tex]17-7x > 3(10x-4)+61\\\\17-7x > 30x-12+61\\\\17-7x > 30x+49\\\\-32 > 37x\\\\x < -\frac{32}{37}[/tex]

So, the values of x are -2, -4, -1.

What is the X
3x +15 and 2x + 20

Answers

Answer:

x = 5

Step-by-step explanation:

What is the X

3x +15 and 2x + 20

assuming that the question is an equation

3x + 15 = 2x + 20

3x - 2x = 20 - 15

x = 5

-----------------

check

3 * 5 + 15 = 2 * 5 + 20

30 = 30

the answer is good

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