if f(x) =7x+5/3-x, then show that fof power -1(x) is an identity function ​

Answers

Answer 1

If f(X)= 7x +5/3 - x =6x +5/3

y= 6x +5/3

6x= y-5/3

f^-1(y)=x=(y-5/3)/6

So we can write

f(f^-1(y))= f((y-5/3)/6) = 6 (y-5/3)/6 +5/3= y-5/3+5/3= y

The same result can be obtained for f^-1(f(x))=x

If the function is f(x)= 7x +5/(3-x) then it is not invertible since it is not injective (pictures)

If F(x) =7x+5/3-x, Then Show That Fof Power -1(x) Is An Identity Function

Related Questions

How do horizontal and vertical translations each affect the coordinates of the points on a figure.

Answers

Answer:

Step-by-step explanation:

Horizontal translations changes the x-axis

Vertical translations changes the y-axis

Gary rents three DVDs each week at Fantastik Flicks. Write an algebraic expression for Wn, the total number of points earned in the nth week

Answers

For the nth week, the total points earned in the DVD rentals is [tex]p_n + 2[/tex]

Your question is not complete, it seems it is missing the following information below;

DVD rentals:         1    2    3    

Total DVD points:  3   5    7    

The number of points earned is a function of number of DVD rentals.

For the first DVD, the number of points earned;

[tex]n_1 = p_1 + c\\\\where;\\c \ is \ the \ constant \ point \ earned[/tex]

3 = 1 + c

3- 1 = c

2 = c

For nth week the total point earned is given as;

[tex]n_t_h = p_n + c\\\\n_t_h = p_n + 2[/tex]

Thus, for the nth week, the total points earned in the DVD rentals is [tex]p_n + 2[/tex]

Learn more here: https://brainly.com/question/18077111

Here we have a problem with arithmetic sequences.

After a small online search, I've found that:

Fantastik Flicks gives: 3 points for the first rental, 5 points for the second rental, 7 points for the third rental

And so on.

We will find that the total of points in the n-th week is given by:

Wₙ = 15 + (n - 1)*18

Looking at the number of points given for each rental, we can see that we have an arithmetic sequence with an increase of 2, 3, 5, 7, 9, 11, 13, 15,...

We want to find the total of points earned in each week. For example, for the first week the total of points is: W₁ = (3 + 5 + 7) = 15

For the second week, the total of points is: W₂ = (9 + 11 + 13) = 33

For the third week, the total number of points is: W₃ = (15 + 17 + 19)  = 51

Now let's see if Wₙ also is arithmetic. To see this, we need to look at the difference between consecutive elements of Wₙ.

W₂ - W₁ = 33 - 15 = 18

W₃ - W₂ = 51 - 33 = 18

So in both cases we got the same difference, this makes a lot of sense, taking in account that we construct the Wₙ with an arithmetic sequence, so is logical that the sequence {Wₙ} is also arithmetical.

Now that we know this, we can see that in the n-th week, the total of points will be: Wₙ = W₁ + (n - 1)*18Wₙ = 15 + (n - 1)*18

If you want to learn more, you can read:

https://brainly.com/question/19007362

CORRECT ANSWER ONLY PLEASE!! What is the simplest radical form of the expression?

(8x5y3)23

Answers

The choose 1.

[tex]4 {x}^{3} {y}^{2} \sqrt[3]{x} [/tex]

I hope I helped you^_^

The simplest radical form of the expression is [tex]4x^2 y^2\sqrt[3]{x}[/tex].

What is simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

When we have indices in the form [tex]ax^{2/3}[/tex] , To find the cube root of the (ax)².

This can be expressed mathematically as

[tex](\sqrt[3]{ax} )^2[/tex]

From the given expression

[tex](8x^5 y^3)^{2/3}\\\\(\sqrt[3]{(8x^5 y^3)})^{2}\\\\4x^2 y^2\sqrt[3]{x}[/tex]

Thus, the simplest radical form of the expression is [tex]4x^2 y^2\sqrt[3]{x}[/tex].

Learn more about an expression here:

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#SPJ2

What decimal is equal to the following fraction?
12/20

Answers

Answer:

It is 0.6

Step-by-step explanation:

[tex] \frac{12}{20} [/tex]

divide numerator and denominator by 2:

[tex] = \frac{12 \div 2}{20 \div 2} \\ \\ = \frac{6}{10} [/tex]

since it's a tenth, it becomes a value with out decimal place:

[tex] = 0.6[/tex]

Write the Roman Numeral CLXIV in standard form. Roman Numeral Standard Number 1 5 10 50 100 500 1,000 X L C D A) 169 B) 166 C) 164​

Answers

Answer:

164

Step-by-step explanation:

in standard form CLXIV IS 164

What is the GCF of 55,40,80?

Answers

5 because 5x11 = 55, 5x8 = 40, and 5x16 = 60

Answer:

Take help of GCF of two or more numbers Calculator to calculate Greatest Common Factor of 55, 80, 40 i.e. 5 largest number that divides all numbers equally.

How many quarts of water should be added to 6
quarts of 80% antifreeze solution to dilute it down
to 30%?

Answers

Answer:

Step-by-step explanation:

Evaluate the expression, given functions f and h:  

f(x) = 3x − 1,

 

h(x) = −2x2 + 3x − 2.

f  

7

3

− h(−2)

resolve into factors:- 49m² + 154m + 121

Answers

Answer:

4m^2 +154m +121

49m^2 +( 77+77)m +121

49m^2 + 77m +77m +121

7m (7m +11) +11 (7m +11)

(7m+11) (7m+11)

hope it was helpful

Answer:

[tex](7m + 11 {)}^{2} [/tex]

Step-by-step explanation:

[tex]49 {m}^{2} + 154m + 121[/tex]

➡️ [tex] {7}^{2} {m}^{2} + 2 \times 7m \times 11 + {11}^{2} [/tex]

➡️ [tex](7 m{)}^{2} + 2 \times 7m \times 11 + {11}^{2} [/tex]

➡️ [tex] = (7m + 11 {)}^{2} [/tex] ✅

collection of even numbers is well defined set or not​

Answers

Answer:

set of even counting number is well-defined

8. The sum of any two consecutive prime numbers is also prime.

Answers

Answer and Step-by-step explanation:

This statement is false because it doesn't apply to all consecutive prime numbers.

Try it yourself.

Take any 2 consecutive numbers, add them together, and see if it is a prime number.

2 + 3 = 5 -- Prime Number

- Factors: 1, 5

3 + 5 = 8 -- Not a Prime Number

- Factors: 1, 2, 4, 8

#teamtrees #PAW (Plant And Water)

I hope this helps!

Describe 2 ways to find the area of the shaded rectangle

Answers

Calculate the area of both shapes. The area of a rectangle is determined by multiplying its length times its width. The area of a circle is Pi (i.e., 3.14) times the square of the radius. Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape.

Evaluate the expression

(x + 3)(y - 2) , if x = -2, and y= 6

Answers

Answer:

The answer is 4

Step-by-step explanation:

Given,

[tex]x=-2,\,y=6[/tex]

Now, the expression

∴[tex](x+3)(y-2)\\=>(-2+3)(6-2)\\=>(1)(4)\\4[/tex]

hope you have understood this...

pls mark my answer as the brainliest

Pleaseee help ill mark brainliest please include explanation too

Answers

Answer:

TO place the triangle ABC on EDF flip the triangle so the you get the mirror image of the triangle and then place it on top of the triangle EDF

hope this helps!

What is the value of the product (3-2i)(3+2i)?

Answers

Answer:

13

Step-by-step explanation:

9-(4i)^2 is the answer

Help plzzzzzzz…………..

Answers

Answer:

-7 + 5 = -2

Step-by-step explanation:

-7 + 5 = -2 is the correct equation as you can see it ended on -2 so in this equation also it's -2

Easy question pls answer​

Answers

Linear pair of angles

how to understand hypabolic equations​

Answers

Answer:

The wave equation utt − uxx = 0 is hyperbolic. The Laplace equation uxx + uyy = 0 is elliptic.

-7 + 4m + 10 = 15 - 2m

what is m?

Answers

ANSWER:
m=2

work shown:

At what input value will the function
f(x) = Vx – 5 + 2 begin to have real
outputs?
x = [?]

Answers

Answer:

x=5 since if anything smaller than 0 it would be an imaginary number and would not be a real output

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

the function of f(x) = √(x – 5) + 2 will have real outputs , since √(x-5) ≥ 0

=> x - 5 ≥ 0

=> x ≥ 5

so, the input value begin from 5


Which names are other ways to name Angle
2?
Select each correct answer

Answers

Answer:

when are you going to insert file?

What is the like terms on this equation

3+5–2x–54-7

Answers

Answer:

3, 5, -54, and -7 are like terms while -2x stays alone.

Step-by-step explanation:

3+5-2x-54-7=0

3+5-2x-61=0

5-2x=61-3

5-2x=59

-2x=59-5

-2x=54

(-x)=54/2

(-x)=27

x=-27

What is the product of 3x+4 and 6x^{2} −5x+7?

Answers

[tex](3x + 4)(6 {x}^{2} - 5x + 7) \\ = 18 {x}^{3} - 15 {x}^{2} + 21x + 24 {x}^{2} - 20x + 28 \\ = 18 {x}^{3} + 9 {x}^{2} + x + 28[/tex]

I hope I helped you^_^

change the decimal into a fraction easy help please :)

Answers

1/5
1/500
1/50
73/100
7/10
773/1000

Jamal buys a strip of 25 postage stamps. The strip of stamps is 21 7/8 inches long. How long is each stamp?

Answers

Rewrite the length as an improper fraction.

21 7/8 = 175/8

Write the quantity of stamps as a fraction: 25/1

Divide length by number of stamps:

175/8 / 25/1

When dividing by a fraction change the sign to multiplication and flip the second fraction over:

175/8 x 1/25.

Now multiply numerators and then denominators:

(175 x1) / (8x 25) = 175/200

Simplify to 7/8

Each stamp is 7/8 inches long

Jim's cat can run 4 blocks in 15 seconds. Juanita says one of her cats can run 3 blocks in 11
seconds. Who has the fastest cat? How did you decide?

Answers

Answer:

Juanita's cat is faster because it can run more blocks in a second

Step-by-step explanation:

Take the number of blocks and divide by the number of seconds

Jim:

4 blocks/ 15 seconds

.26666.... block per second

Juanita

3 blocks / 11 seconds

.2727...... blocks per second

Juanita's cat is faster because it can run more blocks in a second

What is 32,651.97 written in expanded form? PLease dont lie

Answers

Step-by-step explanation:

30000+2000+600+50+1+0.9+0.07

Concept:

First write ten thousands ,then thousands then hundred,then tens then ones then thenths then hundredths.

3. For the sequence defined by tn= 3n + 8,
find each indicated term.
a) t1
b) t7
c) t14

Answers

Step-by-step explanation:

Hi there!

According to the question;

nth term (tn) = 3n+8

a).

T1 = 3*1+8

= 11

b).

t7 = 3*7+8

= 29

c).

t14 = 3*14+8

= 50

Therefore, t1 = 11, t7 = 29, t14 = 50.

Hope it helps!

Answer:

11, 29, 50

Step-by-step explanation:

To find the appropriate term , substitute the term number into the rule, that is

(a) t₁ = 3(1) + 8 = 3 + 8 = 11

(b) t₇ = 3(7) + 8 = 21 + 8 = 29

(c) t₁₄ = 3(14) + 8 = 42 + 8 = 50

How to solve multi step equations

Answers

Answer:

x = –2

Step-by-step explanation:

– 6(1+4x) = –x +40

–6 – 24x = –x +40

24x –x = –6 –40

23x= – 46

x= – 46 / 23

x= – 2

I hope I helped you^_^

A number line shows 1 1/5, −2 2/5, and −1 3/5. Which statement is NOT true?

Answers

Answer:

The answer Is A 1 1/5 < -2 2/5

Step-by-step explanation:

It says that this statement is true because 1 1/5 is to the left of -2 2/5 on the number line but it is actually to the right because -2 2/5 is negative while 1 1/5 is positive therefore making it larger and the correct statement would be that    1 1/5 > -2 2/5

I need help please!!

Answers

Answer:

16 cm2

Step-by-step explanation:

By equa tion of area of triangle: S = 1/2 * height * base

Triangle B: 32  = 1/2 * 8 * x --> x = 8 (cm)

The base of triangle A is half of the base of triangle B so it is 4 cm.

The area of triangle A = 1/2 * 8 * 4 = 16 (cm2)

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