Determine whether f(x) = 3x + 1 and g(x) = (x-1) / 3 are inverses functions. Group of answer choices There are not inverses since both composition equal x. There are inverses since both composition equal x. There are inverses since both composition equal x + 1. There are not inverses since (f (g(x)) = x + 1

Answers

Answer 1

Answer:

They are inverses since both composition equal x.

Step-by-step explanation:

Given the functions, f(x) = 3x + 1 and g(x) = (x-1) / 3, to check if they are inverses functions, we are to find the inverse of one of the function and check if it will give us the other function.

Let's look for the inverse of f(x).

Given f(x) = 3x+1

Let y = f(x) so that y = 3x+1

Replace y with x

x = 3y+1

Make y the subject of the formula of the resulting equation;

3y = x-1

y = (x-1)/3

The new function of x will be the inverse of f(x)

Hence f^-1(x) = (x-1)/3 = g(x)

Another way to check is to find their composition. Let's find f(g(x) and g(f(x)

F(g(x)) = f((x-1)/3)

Replace x with (x-1)/3 in f(x)

F(g(x)) = 3[(x-1)/3]+1

F(g(x)) = x-1+1

F(g(x)) = x

Similarly for g(f(x));

g(f(x)) = g(3x+1)

Replace x in g(x) with 3x+1

g(3x+1) = (3x+1-1)/3

g(3x+1) = 3x/3

g(3x+1) = x.

Since g(f(x)) = f(g(x)) = x, hence f(x) and g(x) are Inverses functions


Related Questions

find the value of x. write your answer in simplest radical form

Answers

Answer:

[tex]x = 4 \sqrt{2} [/tex]

Step-by-step explanation:

To find the value of x we can use either sine or cosine

Using cosine we have

[tex] \cos(\theta) = \frac{adjacent}{hypotenuse} [/tex]

From the question

x is the hypotenuse

4 is the adjacent

We have

[tex] \cos45= \frac{4}{x} \\ x \cos45 = 4 \\ x = \frac{4}{ \cos(45) } [/tex]

We have the final answer as

[tex]x = 4 \sqrt{2} [/tex]

Hope this helps you

Step-by-step explanation:

Sinø=opp/hyp

Sin45=4/x. (× b.s by x)

xSin45=4. (÷ b.s by Sin 45)

x=4/Sin45

x=4.7

The perimeter of a rectangle is 40 m. The length is 4 m more than three times the width. Find the length and the width of the rectangle.

Answers

Answer:

Width = 4 m, Length = 16 m

Step-by-step explanation:

Perimeter = 40

Width = x

Length = 3x + 4

x + x + 3x + 3x + 4 + 4 = 8x + 8

40 - 8 = 32

32/8 = x

x = 4

Width = 4

Length = 16

Please mark as Brainliest, thank you!

18. f-g4, if f =3 and g = -5=

Answers

Answer:

23

Step-by-step explanation:

Step 1:

3 - -5 (4)

Step 2:

3 - (-20)

Step 3:

3 + 20

Answer:

23

Hope This Helps :)

27. Give the perimeter of the rectangle below in
simplest form.

Answers

Answer:

The permeter will be 26 units

Step-by-step explanation:

First to find this you need to know what the value of x is to do this I will use the equation 3x - 7 = x + 2

1. add seven to both sides leaving 3x = x + 9

2. Then subtract the 1x from both sides leaving 2x = 9

3. Then divide 9 by 2 which will be 4.5, x = 4.5

Then just plug 4.5 into each x value 4.5 + 2 and 3(4.5) - 7

1. 4.5 + 2 = 6.5

2. 3(4.5) - 7              13.5 - 7 = 6.5

The perimeter of the rectangle below in simplest form will be 4(x - 3).

Length of the rectangle = 3x - 7

Width of the rectangle = x+2

The perimeter of a rectangle is given as 2(length + width). The perimeter of the rectangle given will then be:

= 2(length + width)

= 2(3x - 7) + 2(x + 2)

= 6x - 14 + 2x + 4

= 4x - 12 = 4(x - 3)

Therefore, the perimeter of the rectangle in simplest form will be 4(x - 3).

Read related link on:

https://brainly.com/question/24429956

what is the answer to
5 1/6 times ( -2/5)

Answers

Answer:-31/15

Step-by-step explanation: step 1: make both fractions improper

step 2: multiply numerator and denominator 31/6 x -2/5= -62/30

step 3: simplify -31/15

Can someone help me simplify 16 > x +9

Answers

Answer:

7 > x

Step-by-step explanation:

16 > x + 9

you subtract 9 from both sides to get your variable by yourself and you keep the same sign

7 > x

Craig has acollection of 220 marbles. He lets his friend have 1/4 of his collection and sells 1/5 of his collection to the novelty store. He takes 15 marbles home to give to his brother. how many marbles remain in Craig's collection? ​

Answers

Answer:

he would have 106

Step-by-step explanation:

hope it helps

What is the coefficient of the x2 term of the algebraic expression 2x4 + x2 - x + 7

Answers

Step-by-step explanation:

2x⁴ + x² − x + 7

= 2x⁴ + 1x² + -1x + 7

The coefficient of the x² term is 1.

Mr.Harris owns a bubble machine that he uses for different school events. The bubble solution contains 3/4 cup of corn starch for every 2 cups of water.

What is the rate in cups of corn starch pero cup of water


A.3/8

B.2/3

C. 1 1/2

D. 2 2/3 ​

Answers

Answer:

3/8

Step-by-step explanation:

Divide 3/4 into 2. Got it right on iready

There are 6 black marbles, 14 blue marbles, 8 white marbles,
and 12 clear marbles in a bag. If Andy chooses a second marble
without replacing the first marble, what is P(black, then clear)?

Answers

Answer:

3/65 = 0.046 = 4.6%

Step-by-step explanation:

Notice that the total number of marbles is:

6 + 14 + 8 + 12 = 40

Then , the probability of getting a black marble first is 6/40 = 3/20

Now, since the experiment is without replacing, he is left with a total of 39 marbles in the bag, and the probability of getting a clear one is now 12/39

The total probability is the product of these two:

(3/20) x (12/39) = 3/65 = 0.046 = 4.6%

-17 = - 10 + x
Help me please

Answers

Answer:

x = -7

Step-by-step explanation:

Isolate x by adding 10 to both sides:

-17 = -10 + x

-7 = x

So, x = -7

A footballer scores in one out of five matches. What percentage of the matches does the footballer score in?

Answers

Answer:

20%

Step-by-step explanation:

100 divided by 5 =20 20x1=20

Bucky received $100 for his birthday. How many hours can he jet ski on Lake Smellsomemore if costs $15
per hour to rent a jet ski and he also has to spend $10 on an inflatable life jacket?

Answers

Answer:

b hours

Step-by-step explanation:

100 minus the 10 on the jacket  equals 90. 90 divided by 15 is 6

What number is the opposite of 3.5

Answers

Answer:

-2/7

Step-by-step explanation: Thats the reciprocal so...


You are buying tickets to a Star Wars Convention. The tickets cost $10 per adult and $3 per child. Parking is a one-time fee of $5. If you
purchased two adult tickets, a, and the total cost was $109, how many child tickets, c, were purchased?

Answers

Answer:

28 children tickets

Step-by-step explanation:

$109 for the whole cost

bought 2 adult tickets that costed 10$ each and payed 5$ for parking fee

add them together 25$

109-25 =84

84/3 =28

calculate the M.A.D WILL BRAINLIST​

Answers

Answer:

24/760/7

Step-by-step explanation:

For the first dataset ...

  d1 = {20, 22, 24, 28, 29, 29, 30}

The deviations from the mean of 26 are ...

  d1 -mean(d1) = {-6, -4, -2, 2, 3, 3, 4}

so the total of the absolute values of these is 24. Since there are 7 numbers, the mean of the absolute deviations is ...

  mad = 24/7

__

For the second dataset ...

  d2 = {12, 15, 21, 30, 33, 35, 36}

The deviations from the mean of 26 are ...

  d2 -mean(d2) = {-14, -11, -5, 4, 7, 9, 10}

so the total of the absolute values of these is 60. Again, there are 7 numbers, so the mean of the absolute deviations is ...

  mad = 60/7

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 lower than in the first. The tax in the first city was
7.5%, and the tax in the second city was 7%. The total hotel tax paid for the two cities was $547.50. How much was the hotel charge in each city before tax?

Answers

Answer:

let the hotel charge before tax for second hotel be x

then the hotel charge before tax for first hotel = x+1500

tax of first hotel = 7.5% * (x+1500) = (7.5x+11250)/100

tax from second hotel= 7% of x = 7x/100

total tax = 547.50

7x/100 + (7.5x+11250)/100 =547.50

14.5x = 54750-11250

14.5x= 43500

x= 3000

hotel charge in first city = 4500

in second city =3000

Step-by-step explanation:

A jar contains 68 marbles, of which 26 are blue, 29 are red, and the rest are green. What is the ratio of green marbles to all marbles?

Answers

the ratio is 13 green marbles to all marbles

Find the value 10 4 exponent

Answers

Answer:
=10^4

=10×10×10×10
=
10
×
10
×
10
×
10

=10000

Order from greatest to least 1.202;1.29;1.02

Answers

Answer:

1.29, 1.202, 1.02

Step-by-step explanation:

1.29
1.202
1.02
hope this helps

Given the points A(-5, -6) and B(8, 2), if C is the midpoint of segment AB, find the coordinates of the midpoint of segment CB

Answers

It’s c bucko I did that

Randell's favorite brand of cookies is on sale at a price of $1.79 for a 12 ounces package. what is the cost per ounce (unit rate) for these cookies?

Answers

Answer:

$0.1492

Step-by-step explanation:

Will give brainliest answer

Answers

4 units to the right and 2 units up is the translation

Answer:

4 and 2 are the correct answers in that order

ILL MARK BRAINLIST !!! SHOW WORK

Answers

Answer:

8748

Step-by-step explanation:

a^5b^-6

when replacing the variables with their values :

3^5 -6^2

3^5 = 3*3*3*3*3 = 243

(-6)^ 2 = 36

243 * 36 =

8748

what is the square route of 36+2

Answers

I believe it is 8 ................

square root 38

Step-by-step explanation:

imput square root 36 plus 2

write a number where the digit 1 greater than the digit 7

Answers

1000-? i think that works

Jean masear is a saw operator in a lumber mill. He works 40 hours a week and earns $630 per week. What is his hourly pay rate

Answers

360/40=15.75 You have to divide 360 in 40

Answer:

[tex]\boxed {\tt \$15.75 \ per \ hour}[/tex]

Step-by-step explanation:

We want to find Jean's hourly pay rate. In other words, his pay per hour.

We can find the pay rate by dividing the money he is paid by the number of hours worked.

[tex]pay \ rate =\frac{money \ paid }{hours}[/tex]

He is paid $630 for 40 hours.

[tex]money \ paid= $630 \\hours= 40\ hours[/tex]

[tex]pay \ rate = \frac{\$630}{40\ hours}[/tex]

Divide.

[tex]pay\ rate = \$15.75 / hour[/tex]

His hourly pay rate is $15.75 per hour.

Please help me out !!!

Answers

Answer:

i cant see the exponent sorry

Step-by-step explanation:

what is the radius of 16\pi

Answers

Id imagine it being 8

Please help me with these two questions.

Answers

Answer:

gooooooooood

Step-by-step explanation:

I kie that

Other Questions
HURRRYYYYYYY!! WILL GIVE BRAINLIESTFind the solution set for the open sentence with the given replacement set. w2+16=8w, {0, 2, 4, 8} 0 2 4 8 Like the Sumerians, the ancient Greeks also farmed, traded, and worshipped many gods and goddesses. However, the Greeks conducted most of their trade via land routes rather than over water.True or False? Last fall, my father went to Japan.Which is the principal part used for the verb went? What sweet food made by bees using nectar from flowers?IF ITS STOLEN FROM A WEBSITE OU ARE GETTING REPORTED. What is a Limited Government? Any number to the power of zero is always? Find the value of x in each case: How do people say goodbye in different French-speaking countries? A square has a side length of 9 cm2 what is the area WHat is appendicitis? Evaluate the expression when y=2 and z=5. 10y to the second power divided by z what is a cumulative gragh You will add numbers that are relevant to your life and then find the square root of that sum in simplified radical form. Find the sums of: A. All of the ages of the people in your household. B. All the digits in your telephone number, including the area code. C. All of the letters in your first name if you let a An online music company offers 15 downloads for $19.75 and 40 downloads for $43.50. Each price includes the same one-time registration fee. What is the cost of each download and the registration fee?what could be the equation What is your role in motivating yourself? What role can others play to help motivate you and help you stay engaged in school? X = 18 is a solution to this equation X + 79 = 98 Question 4 options: True False Assuming the angle below is drawn to scale, which of the following could be the measure of 2XYZ? A. 120 B. 90 C. 180 O D. 30 PLEASE HELP FAST! I'll mark as brainliest 4 4 4 4 = 24 4 4 4 = 34 4 4 4 = 44 4 4 4 = 54 4 4 4 = 6Using only the given operations, make each equation true.Operations: +, -, , , !, %, ^ the cost split among 4 people Can someone help me, please and thank you? I'll give BRAINLEST to the person who gets it right!!!