A function is given:


f(x) = 3x + 12


a. Determine the inverse of this function and name it g(x).

b. Use composite functions to show that these functions are inverses.

c. Evaluate f(g(–2)). Explain: What is the domain?

Answers

Answer 1

Answer:

See explanations below

Step-by-step explanation:

Given the function

f(x) = 3x+12

Let y = f(x)

y = 3x+12

Replace y with x

x = 3y+12

Make y the subject

3y = x-12

y = (x-12)/3

Hence the required inverse is!

g(x) = (x-12)/3

b) To show that the functions are inverses, we must show that f(g(x)) = g(f(x))

f(g(x)) = f((x-12)/3)

Replace x in f(x) with x-12/3

f(g(x)) = 3(x-12)/3 +12

f(g(x)) = x-12+12

f(g(x)) = x

Similarly for g(f(x))

g(f(x)) = g(3x+12)

g(f(x)) = (3x+12-12)/3

g(f(x)) = 3x/3

g(f(x)) = x

Since f(g(x)) = g(f(x)) = x, hence they are inverses of each other

c) Given f(g(x)) = x

f(g(–2)) = -2

The domain is the input variable of the function. Hence the domain is -2


Related Questions

A store in Madison, Wisconsin, advertised an HDTV for $1,224.95.
a. What is the sales tax if the combined state and city rate is 6 percent?
b. What is the total purchase price?

Answers

Answer:

a. $73.50

b. $1298.45

Step-by-step explanation:

6% of $1224.95 is $73.50

add them and it's $1298.45 total

Peter wrote five numbers. Which of peters numbers can be divided into 7 equal groups with 0 left over? Choose that all apply 56, 52, 42, 35, 27,

Answers

Answer:

56

42

35

Step-by-step explanation:

Of 500 seventh grade students, 310 walk to school. What percent of seventh graders do not walk to school?

Answers

Answer:

38%

Step-by-step explanation:

[tex]\frac{Part}{Whole}[/tex] × 100%

500 - 310 = 190

[tex]\frac{190}{500}[/tex] × 100% = 38%

In a sale normall prices are reduced by 10% Natalie brought a pair of shoes from the sale and they cost £54 what was the original price

Answers

Answer: £60

Step-by-step explanation:

Natalie bought a pair of shoes for £54 which had been reduced by 10%.

To find the original cost, assume the original cost is x.

The discount would be: 10% * x

The expression would therefore be:

x - (10% * x) = 54

x - 0.1x = 54

0.9x = 54

x = 54 / 0.9

x = £60

HELP EXPLAIN THIS TO ME

Answers

Answer:

-54 an

Step-by-step explanation:

Answer:

I'm guessing when it says "over the y-axis", it means to reflect it over the y-axis.

In that case, you would graph the points of the triangle, then flip them over the y-axis (change the x-values).

ex. R(-5,3)-R`(5,3)

A rectangle shop in the mall has a perimeter of 36 meters. Its area is 80 square meters. What are the dimensions of the shop?

Answers

Answer:

Length, l = 10 m, breadth = 8 m

Step-by-step explanation:

Let l be the length and b be the width of the rectangle.

The area of a rectangle is given by :

A = lb

80 = lb ...(1)

The perimeter of a rectangle is given by :

P = 2(l+b)

36 = 2(l+b)

18 = (l+b) ....(2)

We need to solve equation (1) and (2). On solving we get :

l = 10, b = 8

So, the dimensions of the shop is 10 m and 8 m.

20x – 10 + 6x - 4
Make the equation smaller

Answers

Answer:

simplify

Step-by-step explanation:

20x-10+6x+4

20x+6x

26x-14

also**

Download the app MathPapa, it really helps me and you can simplify equations.

The answer is 26x-14

cm
squa
(i)
D
5 cm
(ii
4 cm
A
6 cm​

Answers

Answer:

6 squared

Step-by-step explanation:


HELP PLSSSS ILL GIVE U 22 PLSSS HELPO

Answers

Answer: no they are not

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

KM=11-7=4

if parallel, KM/KJ=LN/LJ

substituting:

4/11 is not equal to 3/8

can someone help me with this please?

Answers

The first few are alike

There are 39 students in a class of which 14 are girls,
What fraction of the students is girls?​20 points

Answers

Answer:

it would be 14/39

Step-by-step explanation:

answer: 14/39 hope it helps

Solve for x. Need help please

Answers

Answer:

19

Step-by-step explanation:

1. Both angles would probably add up to 180 degrees.

2. So rewrite this as an equation. (2x + 3) + (9x - 32) = 180

3. Add up like terms like 2x and 9x which would be 11x

4. Rewrite equation again for less confusion. 11x + 3 - 32 = 180

5. Combine like terms again. Like terms this time are 3 and 32

6. 3 - 32 which would be negative 29

7. Rewrite equation again for less confusion. 11x - 29 = 180

8. Add 29 to both sides of equation meaning add 29 to 180.

9. You're left with 11x = 209

10. Divide 209 by 11

11. Lastly you get 19.

I hope this helped and that it's right!

Select the expression that shows the application of the distributive property for

9(t - 5)
a
9t + 14
b
9 + t + 9 + 5
c
9t + 45
d
9t - 45
PLEASE HELP ME!!!

Answers

Answer:

c. 9t+45 that shows distributive property

where it shows a*(b+c)=(a*b)+(b*c).so,9(t+5)=9*t+9*5

LA Galaxy have won 60% of their soccer matches. If they have played 40 matches, how many have they won?

Answers

Answer: LA Galaxy has won 24 of their soccer matches.

Step-by-step explanation:

To find 60% of 40, you can multiply 60/100 by 40.

60/100 x 40 = 24.

In conclusion, LA Galaxy has won 24 of their soccer matches.

Is the relation a function?? Plzz helppp!!!

(1,19) , (2,23) , (3,23) , (4,29) , (5,31)

Answers

Answer: no

Step-by-step explanation: if the y values are the same they are not functions. :) (ps, x values can be the same in a function!)

Answer:

no :)

Step-by-step explanation:

because (2,23) and (3,23) have the same y function

hope this helps!

How do I solve these two complex fraction problems 7/x + 3/2 / 5/x and x+3/3x / x^2-9/6x-9?

Answers

Answer:

x

=

0, 1/3

x=x^3-x/2-9

Step-by-step explanation:

Alvin is 15 years younger than Elga. The sum of their ages is 49. What is Elga's age?

Answers

Answer:

32

Step-by-step explanation:

Suppose Alvin is x years old. Then Elga is x+15 years old.

x+x+15=49

2x=34

x=17

17+15=32

A walkway goes through the middle of a square playground from one corner to the opposite corner. If the walkway is 20 meters long, how long are each of the sides of the playground? Round your answer to the nearest hundredths.

Need Help!

Answers

I think you would use the Pythagorean Theorem to solve this, as a square cut across diagonally creates two isocele triangles. Since the longest side is 20 m, this value would be imputed into c^2.

a^2 + b^2 = c^2
a^2 + a^2 = 20^2
2a^2 = 400
2a^2/2 = 400/2
a^2 = 200
a = 14.14

Thus, each sides of the playground are 14.14 meters long.

helppp

If h = 10 cm and r = 5 cm, then the volume of this cone is___________cm3. (round to the 100th)​

Answers

Answer:

261.8

Step-by-step explanation:

pi x 5 squared x 10/3 = 261.8 for a cone

-__________________________-

Answers

Answer:

minecraft

Step-by-step explanation:

okay I agree with this question

Answer:

thx for the free points

Step-by-step explanation:

have a good day

Mrs. Upton's baby weighs 5 pounds and 4 ounces. How many total ounces does the baby weigh?

Answers

Answer:

84 ounces

Step-by-step explanation:

5 pounds in ounces is 80 plus the 4 ounces is 84

hope this helps

pls mark brainliest

Answer:

84 ounces

Step-by-step explanation:

16 ounces per pound

16 x 5 = 80

80 + 4 = 84

Ill give u brainly if u help on this one too please !

Answers

Answer:

The correct answer is B!

Step-by-step explanation:

I hope it helps you Sir (or ma'am.)

Help with this question plz

Answers

Answer:

A)y=x²-11x+24

Step-by-step explanation:

Question 2
Write an equation in slope-intercept form for the line with slope - 3 and y-intercept - 1.
D=0
.
Х

Answers

Answer:

y=-3x-1

Step-by-step explanation:

Slope-intercept format:

y = mx+b

m = slope

In this case, the slope is -3

b = y-intercept

In this case, the y-intercept is -1

Now we plug it in to get the equation:

y=-3x-1

I hope this helped!

Sincerely,

Rekifromsk8theinfinity

:D

2x-2= 10x -4 help me

Answers

Answer

-8x=-2

x=-2/-8

x=1/4

Step-by-step explanation:

I really need help with trigonometry and laws of sine I’m being timed so please help me

Answers

Answer:

square root of 75, using Pythagorean theorem.

Step-by-step explanation:

An exponential function, f(x), passes through the points (2,5) and (8,20). Determine the value of f(25) to the nearest integer.

Answers

Answer:

assume: f(x) = A(bx); then: f(8) = A(b8) = 20;

and: f(2) = A(b2) = 5

dividing the first equation by the second equation gives: b6 = 4; or: b = 4(1/6) = 1.26;

then: A(1.262) = 5; or: A = 5/(1.262) = 3.15; then: f(x) = 3.15(1.26x);

so that: f(25) = 3.15(1.2625) = 1017.6 ---> 1018

Step-by-step explanation:

hope it helps and Work..

Ana multiplied 24,567 by a secret number. The product was more than 24,567. Select all the numbers that could be the secret number.

Answers

Answer:

what are the numbers..?

Step-by-step explanation:

You have a rental company come and set up a tent for a wedding banquet. Each pole is 7 feet tall and the 20 foot-long rope goes from one stake to an eyelet at the top of the pole and back to the other stake. What is the equal distance each stake will be away from the base of the pole?

Answers

Answer and explanation:

The connection of the rope from the stake to the pole will form a triangle so that one side is the hypotenuse(the rope), another is the opposite side(the pole) and the other is the adjacent side(the distance from the stake to the pole).

The unknown side is the adjacent side which is the distance from the stake to the pole. To find an unknown side in a triangle in this form, we use the Pythagorean theorem.

Therefore c²=a²+b²

c=20ft

a= 7ft

b= unknown

So we use the formula to find unknown side(distance from stake to base of pole)

20²=7²+b²

400=49+b²

b²=400-49

b²= 351

b=√351

b= 18.735ft

Therefore distance from stake to base of pole = 18.735 feet

Four expressions are shown below:


A 21x + 6
B 3(7x + 2)
C 18x + 9
D 3(6x + 3)

Which two expressions are equivalent to 3(6x + 2 + x)? ( by the way i will give brainlist to who ever says the awnser plus say #BRAINLISTPLZ )

Answers

Answer:

B) 3(7x + 2)

Step-by-step explanation:

6x is 6x and x is 1x but you don't usually put the 1 infront of the x.

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