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 many sides does an octagon have

Answers

An octagon has 8 sides (the stop sign is an octagon)
it has 8 sides. (think of a stop sign, like the person said above me, i can’t think of no other objects)

Which names are other ways to name _1? Select each correct answer.

y
pfy
pyf
p
yfp
ypf
f​

Answers

Answer:

your answer is F

I hope it's helps you

can someone please help me with this?

Answers

I think the given figure will help you....

find the distance between P=(4,7) and Q=(1,3)​

Answers

Answer:

may be 5 unit is the distance is between then

Answer:

5 units

Step-by-step explanation:

use distance formula kid

The total bill (parts and labor) for the repair of a car was $458. The cost of parts was $339. The cost of labor was $34 per hour. How many hours of labor did it take to fix the car?​

Answers

Answer:

3.5 Hours MARK ME AS BRAINLIEST PLEASE

Step-by-step explanation:

Take 458, and subtract 339 from it. Then, divide that by 34.

Answer:

3 and a half hours

Step-by-step explanation:

Subtract 399 from both sides

119 = 34h

Divide both sides by 34

3.5 = h

is 4.49 a rational number

Answers

Answer:

yes it is

rational number is any number that can be expressed as a ratio of two integers (hence the name "rational"). It can be written as a fraction in which the the top number (numerator) is divided by the bottom number (denominator).

plsmark me brilliant

A new business had a profit of $6,500 in the first month, a loss $1,200 in the second month and a loss of $1,300 in the third month. What is the net profit or net loss over the first three months​

Answers

Answer:

$4000 net profit

Step-by-step explanation:

Profit adds to the net revenue, while loss subtracts from it.

So 6500 is positive but 1200 and 1300 are negative.

+6500 - 1200 - 1300 = 5300 - 1300 = 4000

$4000 profit

Write 0.2 as a fraction in simplest form.

Answers

Answer:

It is 1/5

Step-by-step explanation:

0.2 is a decimal ( tenth value [1/10] )

[tex]0.2 = \frac{2}{10} [/tex]

divide the fraction ( numerator and denominator ) by 2:

[tex] = \frac{2 \div 2}{10 \div 2} \\ \\ = \frac{1}{5} [/tex]

help please asap lol thanks​

Answers

Answer:

3.3

Step-by-step explanation:

Find all the numbers and find the mean

The x means that there are that many of each number

1 + 1 + 2 + 3 + 3 + 4 + 4+ 5 + 5 + 5

33

We have to divide that by the total amount of numbers present

33/10 = 3.3

the yearly membership to the san diego zoo for a family with 2 adults and 2 children is $144. the regular admission to the zoo is $18 for each adult and $8 for each child. how many times should such a family plan to visit the zoo in a year to make a membership less expensive than paying regular admission?

Answers

The cost of a single visit = 2 x 18 + 2 x 8 = $52
Two visits would cost $104 at regular rate
Three visits would cost $156

If the family visits the zoo more than twice it would be cheaper to have a membership.

Solve the given equation for X.
X/3 + X/7 = 5/3

Answers

The answer is 7/2
In decimal form it’s 3.5

Answer: x = 3.5

Step-by-step explanation:

Given

x/3 + x/7 = 5/3

Determine the Least Common Multiple (LCM) of the denominators

First 10 multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

First 5 multiples of 7: 7, 14, 21, 28, 35

Since 21 is the first overlapping term in both lists, therefore, 21 is the LCM of 3 and 7.

Multiply Least Common Multiple (LCM) of the denominators on both sides

21 (x/3 + x/7) = 21 × 5/3

Expand parentheses and apply the distributive property

7x + 3x = 35

Combine like terms

10x = 35

Divide 10 on both sides

10x / 10 = 35 / 10

[tex]\boxed {x=3.5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Five times the sum of a number and 7 is 8

Answers

Answer:

(x + 7) 5 = 8

Step-by-step explanation:

A number = x

Sum = addition

(x + 7)

Five times would be

(x + 7) 5

And if equivalent to 8 then…

(x + 7) 5 = 8

Are (2,9) and (-3,-6) both on the line y = 4x + 6? If not, find an equation for the line that does pass through both points.

Answers

Answer:

no, y=3x+3

Step-by-step explanation:

plug both points into the equations:

9=4*2 +6 -> 9=8+6, doesn't work-6=4(-3)+6 -> -6=-6, works

one works but the other doesn't so now we find a line through both points

use the formula (y_2-y_1)/(x_2-x_1) to find the slope:

(-6-9)/(-3-2)=-15/-5=3

y=3x+b, plug in a point to find b:

9=3(2)+b9=6+bb=3y=3x+3

Perimeter?
2cm
55mm
10cm
60mm

Answers

a = 2 cm

b = 55 mm = 5,5 cm

c = 10 cm

d = 60 mm = 6 cm

Perimeter: 2 + 5,5 + 10 + 6 = 23,5 cm

Construct a line that is perpendicular to
AB and passes through point X.

-I really need help I’m crying at the moment :/

Answers

1) The line will need to be vertical down the point of x, meaning draw a line down point x. Perpendicular lines look similar to t’s
2.) Same thing, just draw a line through point O and the line. They should look similar to t’s
Hope this helped!! I understand math can get really hard, soon it’ll all be over :)

Kris drives 30 miles to work. For the first x miles, he drives 40 miles per hour. Then he is stuck in traffic and averages only 3 miles per hour the rest of the way. This expression can be used to find the total time Kris spends commuting: 40(x) + 3(30 - x).

Simplify the expressions.

1. 3(30 – x)


2. 40(x) + 3(30 - x)

Answers

I'm sorry if it's not quite right.

Answer:

1) -3x + 90

=(3)(30+−x)

=(3)(30)+(3)(−x)

=90−3x

=−3x+90

2) 37x+90

=40x+(3)(30)+(3)(−x)

=40x+90+−3x

Combine Like Terms:

=40x+90+−3x

=(40x+−3x)+(90)

=37x+90

what is the rule division property of radicals?

Answers

Answer:

Divide the numbers from within the radicals.

Ms. Ferris owns a barn 12 yards long

Answers

Answer:

V = 1188 yd^3

Step-by-step explanation:

The volume or a rectangular prism is given by V = l*w*h V = 12 (9) * 11 V = 1188 yd^3  

Read more at Answer.Ya.Guru – https://answer.ya.guru/questions/6458403-msferris-owns-a-barn-12-yards-long-9-yards-high-and-11-yards.html

Express each percent as a fraction or mixed number in simplest form.
120%
++pls explain how to do this if you know​

Answers

Answer:

120/100

Step-by-step explanation:

120÷20= 6

100÷20=5

6/5 = 1⅕

1+sin^4-cos^4a/1-sin^6-cos^6a=2/3cos^2a​

Answers

Answer:

Step-by-step explanation:

From what I can come up with with no actual factual information is that the equation is

[tex]\frac{1+sin^4x-cos^4x}{1-sin^6x-cos^6x}=\frac{2cos^2x}{3}[/tex] I'm going with that because it actually solves pretty easily, which is usually the way this goes. Begin by cross multiplying:

[tex]3(1+sin^4x-cos^4x)=2cos^2x(1-sin^6x-cos^6x)[/tex] and distribute:

[tex]3+3sin^4x-3cos^4x=2cos^2x-2cos^2xsin^6x-2cos^8x[/tex] and then break up the powers of sin into squared sines:

[tex]3+3[sin^2x*sin^2x]-3cos^4x=2cos^2x-2cos^2x[sin^2x*sin^2x*sin^2x]-2cos^8x[/tex]  and use the Pythagorean identity to change those sines into cosines:

[tex]3+3[(1-cos^2x)(1-cos^2x)]-3cos^4x=2cos^2x-2cos^2x[(1-cos^2c)(1-cos^2x)(1-cos^2x)]-2cos^8x[/tex]

and the FOIL out those terms inside the square brackets:

[tex]3+3[1-2cos^2x+cos^4x]-3cos^4x=2cos^2x-2cos^2x[1-3cos^2x+3cos^4x-cos^6x]-2cos^8x[/tex]

and distribute again on both sides to get rid of the brackets entirely:

[tex]3+3-6cos^2x+3cos^4x-3cos^4x=2cos^2x-2cos^2x+6cos^4x-6cos^6x+2cos^8x-2cos^8x[/tex]

and combining like terms cancels a lot of that out to leave:

[tex]6-6cos^2x=-6cos^6x+6cos^4x[/tex] and get everything on one side to factor:

[tex]0=-6cos^6x+6cos^4x+6cos^2x-6[/tex] and factor out the -6:

[tex]0=-6(cos^6x-cos^4x-cos^2x+1)[/tex] and now we'll factor by grouping, so grouping everything together to get ready for that:

[tex]0=-6[(cos^6x-cos^4x)-(cos^2x+1)][/tex] and begin the factoring:

[tex]0=6[cos^4x(cos^2x-1)-1(cos^2x-1)][/tex] and continuing the factoring:

[tex]0=-6(cos^2x-1)(cos^4x-1)\\0=-6(cos^2x-1)(cos^2x-1)(cos^2x+1)[/tex] and by the Zero Product Property (and we won't list that duplicated factor cuz it's not necessary):

[tex]cos^2x-1=0[/tex]     or       [tex]cos^2x+1=0[/tex]

Solving the first:

[tex]cos^2x=1[/tex] so

x = 0 + 2kπ  and solving the second one:

[tex]cos^2x=-1[/tex] which is not solvable over the real number system.

So x = 0 + 2kπ

and I really hope that's what you were looking for!

hi please help i’ll give brain

Answers

Answer:

The GCF is going to be 2

Step-by-step explanation:

This Is how I find the GCF of 3 numbers. I find the prime factorization first, then I find the common factors and multiply them. Here

The prime factorization of 8, 2 × 2 × 2 = 8

The prime factorization of 18, 2 × 3 × 3 = 18

The prime factorization of 70, 2 × 5 × 7 = 70

The one and THE only common factor is 2, which is going to be the GCF

What’s the answer to this? Please send help

Answers

Answer:

But I see no attachment....pls recheck

geometry help pls
How do you say DE = FG?
can someone explain why

Answers

Answer:

first option

Step-by-step explanation:

congruency has its own symbol and it's a ~ top of a = sign. and the expression doesn't have the symbol. so we can eliminate two options out meaning it's a.

The correct answer would be an option (A) the measure of segment DE is equal to the measure of segment FG.

What are congruent triangles?

Two triangles are said to be congruent if their corresponding sides and angles are equal.

SSS stands for Side-Side-Side criterion. According to this, two triangles are congruent if three sides of a triangle are equal to the corresponding sides of the other triangle.

SAS stands for Side-Angle-Side criterion.  According to this, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

Given that, DE = FG

Congruency is represented by its own symbol, which is a ~ sign on top.

Here, Segment FG's measure is equal to segment DE's measure.

There is no symbol assigned to the expression. Since two possibilities are no longer an option, it must be Option (A).

Hence, the measure of segment DE is equal to the measure of segment FG

Learn more about of congruent triangles here:

brainly.com/question/4364353

#SPJ5

b. The number of cats your teammates have as pets: 0, 1, 3,2

Answers

Ok so 1.2 is the answer you get if you divide them

and you can also say one because its counting by ones

i hate math ( ◠‿◠ )
help me PLS

Answers

Answer:

g=Xs+t

Step-by-step explanation:

please love math

to learn math, to look for topics you don't know in the internet

If n - 72 = 36, then what is the value of n?

Answers

N - 72 = 36

To solve for n add 72 to both sides of the equation:

N = 108

Answer:

108

Step-by-step explanation:

Add 72+ 36 you will get your answer

The answer is 108

Therefore n= 108

golf activity geometry
use distance formula
HELP PLEASE n explain if you know!

Answers

Answer:

Step-by-step explanation:

What numbers are 3 units from -2 on a number line?

A number line ranging from negative 10 to positive 10

Select from the drop-down menus to correctly complete the statements.

______is 3 units left from ​-2 ​ on a number line.

______- is 3 units right from ​-2​ on a number line.

The answers are
-1
-5
1
5
please hurry

Answers

Answer:

___-5___is 3 units left from -2 on a number line.

___1___- is 3 units right from -2 on a number line

Inverse function
G(x)=2x+2

Answers

Answer:

Step-by-step explanation:

y = 2x + 2

x = [tex]\frac{y-2}{2}[/tex]

y = [tex]\frac{x-2}{2}[/tex]

[tex]g^{-1}[/tex] (x) = [tex]\frac{x-2}{2}[/tex]

Please hurry i need a asnwer

Answers

Answer:

[tex] \frac{5i}{3 + 2i} \times \frac{3 - 2i}{3 - 2i} \\ \frac{15i - 10 {i}^{2} }{9 - 4 {i}^{2} } \\ \frac{15i - 10( - 1)}{9 - 4( - 1)} \\ \frac{15i + 10}{9 + 4} \\ \frac{15i + 10}{13} \\ \frac{10}{13} + \frac{15i}{13} [/tex]

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