Find range of the real function
[tex]f = \left \{ \bigg(x, \: \dfrac{ {x}^{2} }{ {x}^{2} + 1} \bigg) : x \: \in \: R \right \}[/tex]
from R into R​.

Answers

Answer 1

Step-by-step explanation:

[tex] \large\underline{\sf{Solution-}}[/tex]

Given function is

[tex]\rm \longmapsto\:f = \bigg(x, \: \dfrac{ {x}^{2} }{ {x}^{2} + 1} \bigg) : x \: \in \: R[/tex]

To find the range of the function f, Let assume that

[tex]\rm \longmapsto\:y = \dfrac{ {x}^{2} }{ {x}^{2} + 1} [/tex]

[tex]\rm \longmapsto\: {yx}^{2} + y = {x}^{2} [/tex]

[tex]\rm \longmapsto\: {yx}^{2} - {x}^{2} = - y[/tex]

[tex]\rm \longmapsto\: - {x}^{2} (1 - y) = - y[/tex]

[tex]\rm \longmapsto\: {x}^{2} (1 - y) = y[/tex]

[tex]\rm \longmapsto\: {x}^{2} = \dfrac{y}{1 - y} [/tex]

[tex]\rm\implies \:x = \sqrt{\dfrac{y}{1 - y} } [/tex]

For x to be defined,

[tex]\rm \longmapsto\:y \geqslant 0 \: \: and \: \: 1 - y > 0[/tex]

[tex]\rm \longmapsto\:y \geqslant 0 \: \: and \: \: - y > - 1[/tex]

[tex]\rm \longmapsto\:y \geqslant 0 \: \: and \: \: y < 1[/tex]

[tex]\bf\implies \:y \: \in \: [0, \: 1)[/tex]

Hence,

[tex]\bf\implies \:Range \: of \: f \: \in \: [0, \: 1)[/tex]


Related Questions

guys pls help me!!!!!!!

Answers

Answer:

5.

Step-by-step explanation:

9y - 6 + 51 = 90

9y + 45 = 90

9y = 45

y = 5.

The answer is y is equal to 5.


The symbol in the corner tells us that the corner is 90 degrees. So much sides added together is 90.
9y - 6 + 51 = 90
9y + 45 = 90
9y = 45
y = 5

What’s 20/10 simplified??

Answers

Answer:

answer is 2

Step-by-step explanation:

20/10

divide both answers by ten

2/1

then one is meaningless so u remove it

Question is in image.
a. x = 4, RS = TS = 23, RT = 7
b. x = 2, RS = TS = 20, RT = 5
c. x = 3, RS = TS = 29, RT = 8
d. x = 5, RS = TS = 18 RT = 4

Answers

Answer:

C.

Step-by-step explanation:

HOPE ITS HELP

whith jrverano2010

HELP ME PLEASE I AM SO DESPERATE THIS IS DUE IN 12 minutes!!!!

Answers

Answer:

3/4

Step-by-step explanation:

4/6 wnwjejjahshswbbshwhehehehs

Can someone answer this for me

Answers

x=60° (equilateral triangle)

y=120°
Working: (360°-120°)/2

The endpoints of are A(2, 2) and B(3, 8). is dilated by a scale factor of 3.5 with the origin as the center of dilation to give image . What are the slope (m) and length of ?

Answers

Answer:

The slopes of both are m=6

Length of AB=6.082

Length of the image: 3.5 * 6.082 = 21.287

Answer:

Step-by-step explanation:

Need help with this ‘

Answers

(-infinity , -8) and (0, infinity)

The length of a rectangle is three more than twice it’s width. The perimeter of the rectangle is 246 cm. Write an equation to find the perimeter and then find the length of the rectangle.

Answers

Answer:

83 cm

Step-by-step explanation:

Let the length of the rectangle be L cm and the width be W cm.

L= 2W +3 -----(1)

Perimeter of rectangle= 2(length) +2(width)

2L +2W= 246 -----(2)

Substitute (1) into (2):

2(2W +3) +2W= 246

Expand:

4W +6 +2W= 246

Simplify:

6W +6= 246

Divide both sides by 6:

W +1= 41

W= 41 -1

W= 40

∴ width of the rectangle is 40cm.

Substitute value of W into (1):

L= 2(40).+3

L= 80 +3

L= 83

Thus, the length of the rectangle is 83 cm.

HELP ASAP 100 POINTS!
Which of the following represents a function?
(-1, 2), (-2, 1), (-1, -2), (-2, -1)
(3, 4), (-3, 2), (3, 8), (5, 5)
(2, 3), (4, 3), (-2, -3), (-4, -3)
(5, 1), (5, 2), (5, 3), (5, 4)

Answers

Step-by-step explanation:

If in any set, you can find 2 or more points that lie on the same vertical,

then it is NOT a function, that is, the same value of x yields 2 or more different

values of y, you don't have a function.

e.g. D is definitely not a function. You have (-2,4) and (-2,-4) , the same x of -2 giving you a y value of 4 and -4.

How do I find all the angles?

Answers

Step-by-step explanation:

so let's say

•(x + 60) = <a

•2x = <b

so

•<a = <z & <b = <y

&

•<a + <b = 180

(x + 60) + 2x = 180

3x + 60 = 180

3x = 180 - 60

3x = 120

x = 40

• <a = (x + 60)

= 40 + 60

= 100

• <b = 2x

= 2 × 100

= 200

• <y = <b

= 200

• <z = <a

= 100

Step-by-step explanation:

so in a 4 sided figure all the angles measure to 360º in total

as well as in this case due to the two lines being parallel z=x+60  and y=2x

The easiest way for me is to write that all the angles = 360.

x+60+x+60+2x=2x=360

6x+120=300                   simplify

6x=180                            divide

x=30

so the angles are all 90º if you find each of them

                                       

Simplify the expression (2x^2+6x-7)-(9x^2-11)

Answers

2x^2 + 6x - 7 - 9x^2 + 11

(2x^2 - 9x^2) + (6x) + (-7 + 11)

-7x^2 + 6x + 4

Hope this helps!! :)

Answer:

=- 7x^2+6x+4

Step-by-step explanation:

HELP ME PLEASE!
Haddad purchases a new surround sound system with a store credit card. If Haddad pays the
minimum monthly payment, he will have his balance paid off in 41 months. If he pays an
additional $15.00 each month, he will have his balance paid off in 27 months. What percent
of time will Haddad save by paying the extra $15.00 per month?
O 15%
O 34%
O 29%
O 66%

Answers

34% is the correct answer
Hope this helps

you have one apple you get another how many do you have cut

Answers

Answer:2

1+1=2

NO WAY

angle M and angle N are complementary. The measure of angle M is 38 degrees less than the measure of angle N Find the measure of each angle.

Answers

Answer:

M = 26 degrees, N = 64 degrees

Step-by-step explanation:

When 2 angles are complementary, it means they add up to 90 degrees. We can set up a system of equations to represent the situation.

M is measure of angle M

N is measure of angle N

M + N = 90 degrees

M = N - 38 (measure of angle M is 38 degrees less than measure of angle N)

We can then use the second equation to substitute in M in the first equation with N - 38

N - 38 + N = 90

2N - 38 = 90

2N = 128

N = 64 degrees

We plug this value back into the first equation to find M

M + 64 = 90

M = 26 degrees

The measure of ∠M and ∠N are 26° and 64° respectively.

What is a supplementary angle ?

Supplementary angles sum to 180°.If two angles are supplementary their sum is 180° and sum of two complementary angles is 90°.

According to the given question angle M and angle N are complementary.

Sum of these two angles ∠M + ∠N = 90°.

Assuming measure of ∠N to be x°,So the measure of ∠M is (x-38)°.

Therefore, x + (x-38) = 90°.

2x = 90° + 38°

2x = 128°.

x = 64°.

∴ The measure of ∠M is (64 - 38 )° = 26°.

learn more about angles here :

https://brainly.com/question/7116550

#SPJ2

A tree grew from a height of 6 feet to 15 feet. By what percent did its height increase?

Answers

Answer:

It increased by 150%

Step-by-step explanation:

In the equation x + 10 = 22, what do you need to do to solve the problem ?

Answers

Just move 10 other side
X= 22-10 = 12
It called Substract propertie

Answer:

In the given equation we need to find out the value of x to make this equation true.

First write the equationx+10 = 22Now place 10 to the other side[By placing 10 to the other side the symbol will change into -]x = 22-10Now subtract 10 from 22x = 12∴ 12 + 10 = 22

One fourth of a Number decreased by three is at least two.

Answers

Answer:

100

Step-by-step explanation:

1/4 of 100 is 25. 25-3=22, which is at least 2.

Proportions: If 7.5 cups sugar to make 14 dozen cookies, find K please

Answers

Answer:

8987678

Step-by-step explanation:

Can someone pls help me

Answers

>> Answer

__________

[tex] \: [/tex]

a² = c² - b²

a² = 9² - (√65)²

a² = 81 - 65

a² = 16

a = √16

a = 4

Use Pythagorean theorem

[tex]\\ \sf\longmapsto P^2=9^2-(√65)^2[/tex]

[tex]\\ \sf\longmapsto P^2=81-65[/tex]

[tex]\\ \sf\longmapsto P^2=16[/tex]

[tex]\\ \sf\longmapsto P=4[/tex]

Someobe pleaseeee help I need it​

Answers

Answer:

its 35

Step-by-step explanation:

Could I get help with 8-11 please :(

Answers

Answer:

8. m∠1 = 64, m∠2 = 26, m∠3 = 36

9. m∠1 = 73, m∠2 = 58, m∠3 = 107, m∠4 = 49, m∠5 = 131

10. m∠1 = 34, m∠2 = 52, m∠3 = 38, m∠4 = 94, m∠5 = 56, m∠6 = 38

11. m∠1 = 62, m∠2 = 71, m∠3 = 109, m∠4 = 35, m∠5 = 109, m∠6 = 29, m∠7 = 47, m∠8 = 62

Step-by-step explanation:

8. m∠1 = 180 - (75 + 41) = 180 - 116 = 64

m∠2 = 90 - 64 = 26

m∠3 = 90 - 54 = 36

9. m∠3 = 180 - 73 = 107

m∠1 = 73

m∠2 = 180 - (73 + 49) = 180 - 122 = 58

m∠4 = 49

m∠5 = 180 - m∠4 = 180 - 49 = 131

10. m∠6 = 90 - 52 = 38

m∠3 = m∠6 = 38, m∠2 = 52

m∠5 = 180 - (86 + 38) = 180 - 124 = 56

m∠1 = 90 - 56 = 34

m∠4 = 180 - (34 + 52) = 180 - 86 = 94

11. m∠2 = 71

m∠3 = m∠5 = 180 - 71 = 109

m∠1 = 180 - (47 + 71) = 180 - 118 = 62

m∠4 = m∠2 - 36 = 71 - 36 = 35

m∠6 = m∠2 - 42 = 71 - 42 = 29

m∠7 = 47

m∠8 = m∠1 = 62

Eight people are competing in an art contest for 1st, 2nd, and 3rd place awards. How many
different combinations of awards are there?

Answers

Answer:

24 Combinations

Step-by-step explanation:

There are 8 people and there is a possibility that each can be either 1st, 2nd, 3rd. You would multiply 8 x 3 to get 24 or add 3 eight times

A blank 2-column table with 3 rows. Column 1 is labeled Column A and Column 2 is labeled Column B. A blank graph has label B on the x-axis and label A on the y-axis. Weather data is collected to analyze wind speed according to temperature. Identify the variables as either input or output to label the table and graph. Column A = Column B = Label A = Label B =

Answers

A= temperature column B= wind speed. Label A= wind speed label B= Temperature

10. Write About It Meredith describes to Liza two purchases she made.
"On Monday, I bought 39 books and 21 CDs for $396. On Tuesday, at the
same prices, I bought 52 books and 28 CDs for $518."
Liza thought about the numbers and said, "That's impossible!" Is Liza
correct? Assume that all books cost the same amount and all CDs cost
the same amount. Explain.

Answers

Answer:

Yes, because the 39 books and 21 cds price is proportional to the 52 books and 28 cds' price

Step-by-step explanation:

:>

What are the values of v and w?

Answers

W is 61 because both sides are the same, the two lower angles are the same.

Then 3 angles equal 180.

61 + 61 + v = 180

122 + v = 180 (subtract 122)

V = 58

8.90 x 3.12 will give brainlist

Answers

27.768

Multiply 890 and 312

This equals 277680

We know that there were 4 numbers behind a decimal point

Therefore the last four numbers of 277680 need to be behind a decimal point as well

So you're answer is 27.7680 or 27.768

what is (x^2+2)(5x+1) multipyed

Answers

Answer:

[tex]5x^{3} + x^{2} + 1 0 + 2[/tex] Is the correct answer

Step-by-step explanation:

in pic

(Credit: Symbolab)

(Hope this helps can I pls have brainlist (crown)☺️)

(x²+2)(5x+1) =5x³+x²+10x+2

hope it helps

determine if the givem binomial x-c is a factor of the given polynomial p(x)
[tex]p(x) = {x}^{4} - {x}^{3} + {x}^{2} + x - 1: x - 2[/tex]

​​

Answers

i’m doing the same thing!

The graph of y=mx is a straight line :
(a) Parallel to the x-axis.
b) Passing through the origin
(c) parallel to the y-axis.
(d) coincides with the x-axis.​

Answers

Given :-

The graph of y=mx is a straight line :(a) Parallel to the x-axis.b) Passing through the origin(c) parallel to the y-axis.(d) coincides with the x-axis.

To find :-

The correct option .

Solution :-

General Equation of slope intercept form ,

y = mx + c .

Here c = 0 , so its y intercept will be (0,0) . Hence it will pass through origin .

will pass through origin.

Please tell me the answer up to e no.​

Answers

(I think you need a-e, if not let me know and I will edit accordingly)

a: Divide both sides by 4

cm -> 12:8

3:2

b: Convert and divide both sides by 3

cm -> 150:9

50:3

c: Convert and divide both sides by 20

cm -> 100:80

5:4

d: Convert and divide both sides by 4

months -> 4:12

1:3

e: Convert and divide both sides by 250

g -> 2000:250

8:1

Hope this helps, have a nice day :)

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