Let = {1, 2, 3, 4, 5} be a set. Consider the functions = {(1,3), (2,5), (3,3), (4,1), (5,2)} and = {(1,4), (2,1), (3,1), (4,2), (5,3)} From into . (i) Determine the range of and (ii) Find the composition functions ∘ and ∘ .

Answers

Answer 1

g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}. And the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.

How to solve the problem?

(i) To determine the range of a function, we need to find all the possible output values of the function. In other words, we need to find the set of all second elements in the ordered pairs of the function. For the function f, the set of all second elements is {3, 5, 1, 2}. For the function g, the set of all second elements is {4, 1, 2, 3}. Therefore, the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.

(ii) To find the composition functions f ∘ g and g ∘ f, we need to apply the functions in the correct order. The composition function f ∘ g means that we first apply g and then apply f to the result. The composition function g ∘ f means that we first apply f and then apply g to the result.

For f ∘ g:

First, we apply g to the domain of f.

(1,3) is mapped to (4,2) by g

(2,5) is mapped to (1,4) by g

(3,3) is mapped to (1,4) by g

(4,1) is mapped to (2,1) by g

(5,2) is mapped to (3,1) by g

Now we apply f to the result of g.

(4,2) is mapped to 2 by f

(1,4) is mapped to 4 by f

Therefore, f ∘ g is the function {(1,4), (4,2)}.

For g ∘ f:

First, we apply f to the domain of g.

(1,4) is mapped to 3 by f

(2,1) is mapped to 5 by f

(3,1) is mapped to 3 by f

(4,2) is mapped to 1 by f

(5,3) is mapped to 2 by f

Now we apply g to the result of f.

3 is mapped to (1,2) by g

5 is mapped to (2,1) by g

1 is mapped to (4,2) by g

2 is mapped to (5,3) by g

Therefore, g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}.

Note that the composition functions f ∘ g and g ∘ f are not the same. In general, composition of functions is not commutative, i.e., f ∘ g is not equal to g ∘ f.

To know more about range visit :-

https://brainly.com/question/26098895

#SPJ1

Related Questions

An air traffic controller is tracking two planes. To start, Plane A is at altitude of 2639 feet and Plane B is just taking off. Plane A is gaining altitude at 35.25 feet per second and Plane B is gaining altitude at 80.75 feet per second
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when they're at the same altitude?

Answers

Answer:

Step-by-step explanation:

To find the number of seconds it will take for the planes to be at the same altitude, we need to set the altitude equations for both planes equal to each other and solve for time:

2639 + 35.25t = h (altitude equation for Plane A)

0 + 80.75t = h (altitude equation for Plane B)

where h is the altitude of both planes when they are at the same altitude, and t is the number of seconds that have passed.

Setting the two equations equal to each other and solving for t, we get:

2639 + 35.25t = 80.75t

45.5t = 2639

t = 58

Therefore, it will take 58 seconds for the planes to be at the same altitude.

To find their altitude at that time, we can substitute t = 58 into either of the altitude equations and solve for h:

2639 + 35.25t = h

2639 + 35.25(58) = h

h = 4818.5

Therefore, when the planes are at the same altitude, their altitude will be approximately 4818.5 feet.

To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B.

The mean braking distance for Make A is 42 feet. Assume the population standard deviation is 4.6 feet.

The mean braking distance for Make B is 45 feet. Assume the population standard deviation is 4.3 feet.

At α = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles?

Assume the samples are random and independent, and the populations are normally distributed.

(a) Identify the claim and state H_0 and H_a

(The mean braking distance is different for the two makes of automobiles.)

What are H_0 and H_a?

(b) Find the critical value(s) and identify the rejection region(s).

(c) Find the standardized test statistic z for μ_1 - μ_2

z = _____

(d) Decide whether to reject or fail to reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

Answers

Upper Critical Value; 1.645

p-Value; 0.0814

Reject the null hypothesis

How to solve

a).

claim: A. The mean breaking distance is different for the two makes of automobiles

H0 and Ha.: E

[tex]\ H_0: \mu_1 = \mu_2 \ \ \ H_a: \mu_1 \neq \mu_2[/tex]

b).

critical values are (-1.645, 1.645)

Rejection region: E. z < -1.645 , z >1.645

test statistic z= -1.743

d).

C. Reject H0. The stat statistic falls in the rejection region.

e).

At the 10% significance level, there is sufficient evidence to support the claim that means breaking distance of make A is different from mean breaking distance of making B.

m 2

Z Test for Differences in Two Means

Data

Hypothesized Difference

Level of Significance

0.1

Population 1 Sample

Sample Size

Sample Mean

Population Standard Deviation

4.9

Population 2 Sample

Sample Size

Sample Mean

Population Standard Deviation

4.7

Intermediate Calculations

Difference in Sample Means

-2

Standard Error of the Difference in Means

1.1477

Z Test Statistic

-1.7427

Two-Tail Test

Lower Critical Value

-1.645

Upper Critical Value

1.645

p-Value

0.0814

Reject the null hypothesis

Read more about null hypothesis here:

https://brainly.com/question/25263462

#SPJ1

Find the equation of a line parallel to 5x+y=5 that passes through the point (8,-9)

Answers

Answer:

y = -5x + 31

Step-by-step explanation:

To find the equation of a line parallel to the line 5x + y = 5, we first need to rearrange it in slope-intercept form, which is

y = -5x + 5. (We see that the slope of this line is -5)

A line parallel to this line will have the same slope of -5. Now, we need to find the equation of a line that passes through the point (8,-9) with slope -5.

We can use the point-slope form of the line to find the equation. The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Substituting the values we have, we get:

y - (-9) = -5(x - 8)

Simplifying this equation, we get:

y + 9 = -5x + 40

y = -5x + 31

Therefore, the equation of the line parallel to 5x + y = 5 that passes through the point (8, -9) is y = -5x + 31.

y = -x + 10 y = -x + 12

Answers

The solution to the given simultaneous equation y = -x + 10 ; y = -x + 12 is zero.

How to solve simultaneous equation?

y = -x + 10

y = -x + 12

Subtract both equations

y - y = -x -(-x) + 10 -12

0 = -x + x - 2

0 = 0 - 2

0 = -2

In conclusion, zero is the solution to the equation

Answers

The equation represents the line of best fit is y = -2x + 22.

What is an equation?

A mathematical statement that represents a relationship between two or more quantities is typically expressed using symbols, numbers, and mathematical operations. Equations are used to express mathematical relationships, make predictions, and solve problems. An equation typically consists of an expression on each side of an equal sign (=), indicating that the values on both sides are equivalent.

According to the given information:

To determine the equation of the line of best fit in the scatter plot, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given that the line of best fit goes through points (5, 12) and (9, 4), we can calculate the slope (m) using the formula:

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

Plugging in the values from the given points, we get:

m = [tex]\frac{(4-12)}{(9-5)}[/tex]

m = -8 / 4

m = -2

So, the slope of the line of best fit is -2.

Next, we can substitute the slope and one of the given points (5, 12) into the slope-intercept form to solve for the y-intercept (b):

12 = -2(5) + b

12 = -10 + b

b = 12 + 10

b = 22

So, the y-intercept of the line of best fit is 22.

Thus, the equation of the line of best fit is:

y = -2x + 22.

To know more equation visit: https://brainly.com/question/10413253

#SPJ1

Calculus derivatives. Find f(x).

Answers

The solution equates to f(x) = 6x + 8.

How to explain the function

Reiterating the same statement without reiteration, it is observed that f'(x) equals ƒ""(x), ultimately resulting in a value of 6. Subsequently, we can derive a complete expression for f(x) where C represents an integration constant.

It should be noted that to find this constant, since f(-1) = 2, plugging in x as -1 and f(x) as 2 into the above equation results in:

2 = 6(-1) + C

C = 8

As such, we can confirm that the entire expression of f(x) is simply 6 times x added to 8. Validating this answer, when assessing f(0) or f(1) , either result should match the given values from our initial problem which they do. Hence, the solution equates to:

f(x) = 6x + 8.

Learn more about functions on

https://brainly.com/question/11624077

#SPJ1

Find the x-intercept and y-intercept of this equation.

y = 4x + 7

Question 10 options:

x-intercept (4,0), y-intercept (0,7)

x-intercept (-7,0), y-intercept (0,-4)

x-intercept (7/4, 0), y-intercept (0,-4/7)

x-intercept (-7/4, 0), y-intercept (0,7)

Answers

The intercepts of the equation are: D. D. x-intercept (-7/4, 0), y-intercept (0,7).

What is the X-intercept and Y-intercept of a Linear Equation?

The x-intercept of an equation is simply the value of x when the corresponding value of y equals zero. Also, this is where the line of the equation cuts across the x-axis on a graph.

The y-intercept of an equation, on the other hand, is the value of y when the corresponding value of x equals zero. It is the point where the line of the equation cuts across the y-axis on a graph.

Thus, given the equation y = 4x + 7, the y-intercept is:

y = 4(0) + 7

y = 7

The x-intercept is:

0 = 4x + 7

-4x = 7

x = 7/-4

x = -7/4

The correct option is: D. x-intercept (-7/4, 0), y-intercept (0,7).

Learn more about x-intercept on:

https://brainly.com/question/24363347

#SPJ1

In January, the amount of snowfall was 5 2/3 feet. In February, the amount of snowfall was 3 1/5 feet. What was the amount of snowfall in the two months combined? Write your answer as a mixed number in simplest form.

Answers

Answer:

8 13/15

Step-by-step explanation:

Multiply the fractions so they both have the least common denominator:

5 2/3 = 5 10/15

3 1/5 = 3 3/15

Now, you can add the two mixed numbers:

[tex]5 \frac{10}{15} + 3 \frac{3}{15} = 8 \frac{13}{15}[/tex]

This is your final answer.

A police car is located 40 feet to the side of a straight road.

A red car is driving along the road in the direction of the police car and is 140 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 85 feet per second. How fast is the red car actually traveling along the road?

The actual speed (along the road) of the red car is feet per second

Answers

The actual speed (along the road) of the red car is 8.37 feet per second

To solve this problem

Let's call the distance between the police car and the red car "x" at time t. Then, we know that:

x^2 = 40^2 + (140 - vt)^2

Where

v is the velocity of the red car (in feet per second) t is time

We are given that dx/dt (the rate at which x is decreasing) is -85 ft/s, so:

d/dt [x^2] = d/dt [40^2 + (140 - vt)^2]

2x(dx/dt) = 0 - 2v(140 - vt)

Substituting dx/dt = -85 and solving for v, we get:

2x(−85) = −2v(140−vt)

−170x = −280v + 2v^2t

v^2t = 140v - (85/2)x

Now, we can differentiate the equation x^2 = 40^2 + (140 - vt)^2 with respect to time to get:

2x(dx/dt) = 2(140 - vt)(-v)

Substituting dx/dt = -85 and solving for x, we get:

-170x = -2v(140 - vt)

x = (140v - vt^2)/85

Substituting this expression for x into the equation we derived earlier, we get:

v^2t = 140v - (85/2)((140v - vt^2)/85)

v^2t = 140v - 70(2v - t^2)

v^2t = 140v - 140v + 70t^2

v^2t = 70t^2

v = sqrt(70t^2)/t = sqrt(70) = 8.37 ft/s (rounded to two decimal places)

Therefore, the actual speed (along the road) of the red car is 8.37 feet per second

Learn more about expression here : brainly.com/question/723406

#SPJ1

This diagram shows a cube. Each edge of the cube is 13 units long. The diagonal of each face is x units long. The diagonal of the cube is y units long.

Find x and y. If necessary, round your answers to the nearest tenth.

Answers

The value of x is 18.4 and the value of y is 22.5 in the cube

Finding the values of x and y

From the question, we have the following parameters that can be used in our computation:

The diagram of a cube.

Each edge of the cube = 13 units.

The diagonal of each face is x units long

So, we have

x^2 = 13^2 + 13^2

Evaluate

x = 18.4

The diagonal of the cube is y units long.

So, we have

y^2 = 13^2 + 13^2 + 13^2

Evaluate

y = 22.5

Hence, the value of x is 18.4 and the value of y is 22.5

Answers

Answer:

To convert kilometers per hour to miles per hour, we need to multiply by 0.62. Therefore, to find the maximum speed that Hannah can drive without exceeding the speed limit of 130 kilometers per hour, we can multiply 130 by 0.62:

130 km/h * 0.62 = 80.6 mph

Since Hannah needs to stay within the speed limit, the maximum whole-number speed she can drive is 80 mph, which is option D.

Step-by-step explanation:

it takes 2/3 of a gallon of paint to cover 3/4 of a wall. How many gallons of paint are needed to cover a full wall?

Answers

We can start by using a proportion to find the amount of paint needed to cover a full wall:

(2/3 gallons) / (3/4 of a wall) = (x gallons) / (1 full wall)

To solve for x, we can cross-multiply and simplify:

(2/3) / (3/4) = x / 1

2/3 * 4/3 = x

8/9 = x

Therefore, it takes 8/9 of a gallon of paint to cover a full wall.

The histogram below gives the distribution of test scores for a sample of
students in a school in Alaska. Approximately how many students received a
score between 70.5 and 80?

Answers

Answer:

B. 200 students

Step-by-step explanation:

The perimeter of a rectangle is 21.2 m, and its area is 23.68 m².
Find its length and width.
length: m
width: m

Answers

Perimeter of a rectangle =2(l+w)=21.2m
Area of a rectangle =l*w=23.6m2
21.2=2l+2b————-(eq 1)
23.6=lw—————(eq 2)
l=23.6/w———————(eq 3)
Substitute eq 3 into eq 1
21.2=2(23.6/w)+2w
21.2=47.2/b +2w
Add the right hand side
21.7=(47.2+2w^2)/w
Cross multiply
21.7w=47.2+2w^2

3 A system of two linear equations is graphed on a coordinate plane. If the system of
equations has infinitely many solutions, which statement must be true?
a. On the graph, there are no points (x, y) that satisfy both equations.
b. On the graph, there is exactly one point (x, y) that satisfies both equations.
c. On the graph, any point (x, y) that satisfies one of the equations cannot satisfy the
other equation.
d.
On the graph, any point (x, y) that satisfies one of the equations must also satisfy
the other equation.

Answers

Answer:

d. On the graph, any point (x, y) that satisfies one of the equations must also satisfy the other equation.

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

If the system of linear equations has infinitely many solutions, it means the two lines overlap.

In other words, each point of one of the lines also belongs to the second line.

Choices a, b, c give us one or no solutions and therefore not the answer.

Choice d is reflecting the infinitely many solutions and hence is the correct one.

Calculate the area of the composite figure shown

Answers

The total area of the given figure is 525 cm² respectively.

What is the area?

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

The area of a plane figure is the area that its perimeter encloses.

The quantity of unit squares that cover a closed figure's surface is its area.

So, first, we will divide the figure into 2 parts which will be the triangle and the rectangle, and then add their area to get the total area as follows:

Triangle:

1/2 * b * h

1/2 * 15 * 20

15 * 10

150 cm²

Rectangle:

l*b

15*25

375 cm²

The total area of the figure: 375 + 150 = 525 cm²

Therefore, the total area of the given figure is 525 cm² respectively.

Know more about the area here:

https://brainly.com/question/25292087

#SPJ1

Find the area of the following figure:

Answers

Answer: 61,6 in.

Step-by-step explanation:

To find the area of trapezoids with parallel bases, we add the length of the lower base to the length of the upper base.

[tex]12+10=22[/tex]

Then we multiply this value by the height.

[tex](5.6).22=123.2[/tex]

Finally, we divide the resulting value by [tex]2[/tex].

[tex]123.2/2=61.6[/tex]

Find the area of parallelogram WXYZ. Round your answer to the nearest tenth if
necessary.
21 in
18 in
21 in
23.2 in
23.2 in

Answers

Answer:

378in^2 i think

Step-by-step explanation:

Question
Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function?

Select all correct answers.
Select all that apply:

{(2,−5),(−2,0),(−3,6),(2,−4)}
{(−1,5),(−4,8),(−4,14),(2,6)}
{(1,3),(−2,−1),(4,3),(8,1)}
{(−2,−5),(7,1),(7,−3),(4,−1)}
{(8,8),(4,1),(1,6),(−5,6)}

Answers

Answer:

Step-by-step explanation:

You want the lists of ordered pairs that represent a functional relation.

Function

A function maps an input value to exactly one output value. A set of ordered pairs will represent a function if no input (x-value) is repeated.

We only need to look at the first values of the ordered pairs.

(a) 2 is repeated

(b) -4 is repeated

(c) a function

(d) 7 is repeated

(e) a function

Answer:

Step-by-step explanation:

You want the lists of ordered pairs that represent a functional relation.

Function

A function maps an input value to exactly one output value. A set of ordered pairs will represent a function if no input (x-value) is repeated.

We only need to look at the first values of the ordered pairs.

(a) 2 is repeated

(b) -4 is repeated

(c) a function

(d) 7 is repeated

(e) a function

In a different plan for area codes, the first digit could be any number from 1 through 7, the second digit was either 3, 4, 5, 6, and the third digit could be any number except 6, 7, or 8. With this plan, how many different area codes are possible?

Answers

Answer:

196

Step-by-step explanation:

There are 7 choices for the first spot.

4 choices for the second spot. And 7 choices for the third spot, which cannot be 6,7,8--so it can be 0,1,2,3,4,5 or 9 (7choices)

7 × 4 × 7 is 196

There are 196 possibilities for the three digit area code with this plan.

Please answer quickly!!! I'll give BRAINLIEST!!!!! I attached the picture.

Answers

Answer: No.

Step-by-step explanation:

The graph doesn't represent a linear, exponential, or quadratic function.

An example of a linear function is a straight line.

An example of a quadratic function is like a smile.

An example of an exponential function is a curved line.

So hence, this doesn't represent a function.

Reply below if you have any questions of concerns.

You're welcome!

- Nerdworm

What is the area of a right triangle with a height of 6 1/4 yards and base of 22 yards

Answers

Answer:

The area should be 0.5 * b * h

Step-by-step explanation:

B stands for the base of the triangle and H is the height

If a scatter plot has a pattern that is best fit by y=x2, we say that it has a property that displays a linear or a nonlinear pattern?

Answers

The scatter plot that has a pattern that is best fit by y = x^2 has a property that displays a nonlinear pattern

Describing the property of the scatter plot

From the question, we have the following parameters that can be used in our computation:

Equation of the best fit of the scatter plot: y = x^2

As a general rule

Any equation that has a degree other than 1 is a non linear equation

This means that the property it displays is a nonlinear pattern

Answers

The length of the shadow would be approximately 41.7 feet if the angle of elevation from the horizontal to the sun is 38° at this time.

If the angle of elevation from the horizontal to the sun is 38°, then the tangent of that angle is equal to the opposite side (the height of the tree) divided by the adjacent side (the length of the shadow).

Therefore, we can set up the equation using trigonometric function tangent as,
tan(38°) = height of tree / length of shadow

Solving for the length of the shadow, we get:
length of shadow = height of tree / tan(38°)

Plugging in the given height of the tree (32 feet) and using a calculator to find the tangent of 38°, we get:
length of shadow = 32 / tan(38°) = 41.7 feet (rounded to one decimal place)

Therefore, the length of the shadow would be approximately 41.7 feet at this time.

To learn more about, Trigonometric functions, visit:

https://brainly.com/question/25618616

Betty has 30 mls of cough medicine with breakfast.
She drinks half of her 4 ounce orange juice, and 25% of her 8 oz cup of coffee. How many mls total
did she consume?

Answers

Betty consumed a total of 148.294 milliliters of liquid with her breakfast.

To solve this problem

We can change the volumes of the coffee and orange juice to milliliters so that all of the measurements are in the same unit:

4 ounces = 4 * 29.5735, = 118.294 ml.

8 ounces = 8 x 29.5735, = 236.588 ml.

Half of Betty's 4-ounce glass of orange juice, or:

1/2 * 118.294 mls = 59.147 mls

She consumed 25% of her 8-ounce coffee, which is :

0.25 * 236.588 mls = 59.147 mls.

So, in total, Betty consumed:

30 mls of cough medicine + 59.147 mls of orange juice + 59.147 mls of coffee = 148.294 mls

Therefore, Betty consumed a total of 148.294 milliliters of liquid with her breakfast.

Learn more about milliliters here : brainly.com/question/28920784

#SPJ1

Need help with this problem

Answers

The sales tax on 250 dollars purchase is: $3865

How to find the equation model?

We are told that sales tax is directly proportional to retail price. Thus:

S ∝ p

Any item that sells for 158 dollars has a sales tax of 10.22 dollars. Thus:

158 = 10.22k

where k is constant of proportionality

Thus:

k = 158/10.22

k = 15.46

Thus, the equation is:

S = 15.46p

Sales tax on 250 dollars purchase is:

S = 15.46 * 250

S = $3865

Read more about Equation Model at: https://brainly.com/question/28732353

#SPJ1

how do i find the area of this shape?

Answers

Answer:

(1/2)(12)(16) + (1/2)π(6^2)

= (96 + 18π) square cm

= about 152.55 square cm

what is the value of the expression shown below
2 3/5 - 1 3/5
^ ^
TWO THREE-FIFTHS MINUS ONE THREE-FIFTHS

THE NUMBERS ARE MIXED FRACTIONS

Answers

Answer:

Step-by-step explanation:

1. One way to do this is converting both into improper fractions. To do this, multiply the whole number by the denominator and add that to the numerator.

2 3/5 --> 2*5 is 10 --> 10+3 is 13. --> 13/5

2. This leaves us with 13/5 - 8/5

3. Subtract the numerators

13/5 - 8/5 = 5/5

4. Simplify. If the numerator is the same number as the denominator, it's a whole number.

5/5 = 1

Ms. Shaddai writes 3q = 51 and \{15, 16, 17\} on the board. Tell if each value in the set is a solution of the equation. Show your work.

Answers

Only 17 is a solution of the equation 3q = 51 among the values in the set {15, 16, 17}.

How to find out if each value in the set is a solution of the equation?

To check if a value is a solution of the equation 3q = 51, we substitute the value for q and check if the equation is true.

Let's check each value in the set {15, 16, 17}:

For q = 15, 3q = 3(15) = 45, which is not equal to 51. Therefore, 15 is not a solution of the equation 3q = 51.

For q = 16, 3q = 3(16) = 48, which is not equal to 51. Therefore, 16 is not a solution of the equation 3q = 51.

For q = 17, 3q = 3(17) = 51, which is equal to 51. Therefore, 17 is a solution of the equation 3q = 51.

Therefore, only 17 is a solution of the equation 3q = 51 among the values in the set {15, 16, 17}.

to know more about equation

brainly.com/question/29538993

#SPJ1

Exit
Savvas Realize
8-6: MathXL for School: Practice & Problem Solving
★ Start Page
0 Assignment is past due (
The circumference of the hub cap of a tire is 83.90 centimeters. Find the area of this hub cap. Use 3.14 for x. Use pencil and paper. If the circumference
were smaller, explain how this would change the area of the hub cap.
The area of this hub cap is about 560 square centimeters.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as needed.)

Answers

It can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.

How to solve

Given the circumference (C) of the hub cap as 83.90 cm, we can find the radius (r) using the formula C = 2 * π * r,

where π = 3.14.

Thus, r ≈ 13.363 cm.

To find the area (A), use the formula A = π * r^2, yielding A ≈ 560.509 cm². Rounded, the area is about 561 cm².

Therefore, it can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.

Let = {1, 2, 3, 4, 5} be a set. Consider the functions = {(1,3), (2,5), (3,3), (4,1), (5,2)} and = {(1,4), (2,1), (3,1), (4,2), (5,3)} From into . (i) Determine the range of and (ii) Find the composition functions ∘ and ∘ .​

Answers

Related Questions

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Answers

Let = {1, 2, 3, 4, 5} be a set. Consider the functions = {(1,3), (2,5), (3,3), (4,1), (5,2)} and = {(1,4), (2,1), (3,1), (4,2), (5,3)} From into . (i) Determine the range of and (ii) Find the composition functions ∘ and ∘ .