Are these functions inverses of each other?Be sure to explain how you know they are inverse or why they are not. Show all work necessary.

Are These Functions Inverses Of Each Other?Be Sure To Explain How You Know They Are Inverse Or Why They

Answers

Answer 1

Answer:

Yes. f(x) and g(x) are inverses of one another

Step-by-step explanation:

[tex]f(x) = - \frac{1}{2} x - 2 \\ y = - \frac{1}{2} x - 2 \\ x = - \frac{1}{2} y - 2 \\ x + 2 = - \frac{1}{2} y \\ - 2(x + 2) = - \frac{1}{2} y \times - 2 \\ - 2x - 4 = y \\ {f }^{ - 1} (x) = - 2x - 4[/tex]

In step 1 we just copied the original function.

In step 2 we substituted y for f(x).

in step 3 we switched the variables.

in step 4 we added 2 to both sides.

in step 5 we multiply both sides by -2

In step 6 we solved for y.

In step 7 is just a fancy way of saying the inverse function f(x) = -2x - 4


Related Questions


Amelia went to the candy store and bought 5/6 of a pound of candy. If 1/2 of Amelia's candy
was chocolate, how many pounds of chocolate candy did Amelia buy?

Answers

Answer:

5/12 pounds of chocolate

Step-by-step explanation:

converting 5/6 to 10/12, half of that is is 5/12. hope this helps !!! :D

Answer: 5/12 or about 0.42

Step-by-step explanation:

You are looking for 1/2 of 5/6

5/6 times 1/2 = 5/12

I hope it helps!

A circular table cloth has a radius of 24 inches. Mrs. Lopez is planning to sew a
piece of trim around the edge of the table cloth. To the nearest inch, how much
trim will she need?

Answers

Answer:

150 inches

Step-by-step explanation:

C=2πr

2·π·24 ≈ 150.79645

Mrs. Lopez need to sew a piece of cloth whose length be 150.72 inches.

What is circumference?

A circumference gives the length around a circular object, it is the perimeter used for the circular objects.

Given that a circular tablecloth has a radius of 24 inches, we need to find the length around it,

So, the length around a circular object is its circumference,

We know that circumference of the circular object = π × diameter,

Diameter = 2 × radius = 48 inches.

So, the length around the circular cloth = π × 48

= 3.14 × 48
= 150.72

Hence Mrs. Lopez need to sew a piece of cloth whose length be 150.72 inches.

Learn more about circumference, click;

https://brainly.com/question/28757341

#SPJ2

is this a function? please help

Answers

Where’s the photo. Display a photo or type out the problem.

Question
Use a number line to compare the following fractions: 4/3 7/6

Answers

The comparison is that:

4/3 is greater than 7/6 and 7/6 is less than 4/3

The fractions are given as:

4/3 and 7/6

See attachment for the number line that represents both fractions

From the number line. 4/3 is at the right of 7/6

This means that:

4/3 is greater than 7/6 and 7/6 is less than 4/3

Read more about number lines at:

https://brainly.com/question/10851163

im almost done with this hw. plz help!!! give explanation if you actually know the answer so ik u dont just want points

Answers

Answer:

B

Step-by-step explanation:

That's the only answer that represent the 25% prize rate


Please Help!!!

You shared a bag of fruit snacks with 4 friends. You and each of your friends got 35 or fewer fruit snacks. Solve the inequality below to find the number of fruit snacks that could be in the bag.

Answers

Answer: option 4 x < 175

x/5 < 35

multiply both sides by 5

x < 175

(i can’t do the correct symbol but you get the idea)

Step-by-step explanation:

4×=175

isgsusjisghsusgsbsihhdvejisfehsiwjgsusj

Draw the following triangle after a translation 4 units to the left and 4 units up

Answers

Answer:

just move every corner (vertices) 4 up and 4 to the left

Rewrite -11 + x=7 use the same number just other orders

Answers

Answer:

7 = -11 + x

you can also do x - 11 = 7 or 7 = x - 11

hope these are the rewrites you are looking for

Step-by-step explanation:

PLSSSSSSSSSSSS HELP LAST QUESTION

Answers

Answer:

(12+g)-7

Step-by-step explanation:

Answer:

1. x-5

3. (12+g)-7

sorry don't know number 2

Eric is studying two number patterns. Pattern A starts at 0 and has the rule "add 6." Pattern B starts at 0 and has the rule "add 3." What is the relationship between corresponding terms in the two patterns?

The terms in Pattern B are 3 times the corresponding terms in Pattern A.
The terms in Pattern B are 2 times the corresponding terms in Pattern A.
The terms in Pattern B are one third the corresponding terms in Pattern A.
The terms in Pattern B are one half the corresponding terms in Pattern A.

Answers

Answer:

D) The terms in Pattern B are one half the corresponding terms in Pattern A.

Step-by-step explanation:

Pattern A | Pattern B

0 divided by 1/2 = 0

6 divided by 1/2 = 3

12 divided by 1/2 = 6

18 divided by 1/2 = 9

24 divided by 1/2 = 12

Find m Measure of angle A =

Answers

Answer:

a = 104

Step-by-step explanation:

a = 104 because it is an inscribed angle with an arc of 208 degrees

Danny flips four well-balanced coins. What are the odds that two of the coins will land ‘heads’ up?

Answers

Answer:

0.375 = 37.5% probability that two of the coins will land ‘heads’ up

Step-by-step explanation:

For each coin, there are only two possible outcomes. Either it lands heads, or it lands tails. The probability of a coin landing heads is independent of any other coin. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Four well-balanced coins.

This means that [tex]n = 4, p = 0.5[/tex]

What are the odds that two of the coins will land ‘heads’ up?

This is P(X = 2).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.5)^{2}.(0.5)^{2} = 0.375[/tex]

0.375 = 37.5% probability that two of the coins will land ‘heads’ up

what does 3 x 2/5 equal?

Answers

Answer:

you would get 1.2

Answer:

Step-by-step explanation:

exact form 6/5

decimal form 1.2

mixed number form 1 1/5

Which functions have a period of 2 pi

Answers

Answer:

yes

Step-by-step explanation:

How do I solve this problem?And if a bot puts a link on my question,then what i'm going to do is report the bot.

Answers

Answer : 56.22


So Chris borrowed $88.00

Then from those $88 he had to give his grandparents $31.78 so you can do :

88 - 31.78

Which would give you 56.22 and that is the amount he owes them.

Find the area of this circle. Use 3 for .
A = 7r2
10 ft
[?] ft2
PLEASE HELP

Answers

Answer:

7.0686

your welcome :D.

                                                                                                                                           

PLSSS HELP (4x - 1)
(3x)

Answers

Answer:

x = 13

Step-by-step explanation:

3x + 4x-1 +90 = 180

7x = 91

x = 13

Math problem 8/3+(-9/4)​

Answers

Answer:

[tex]\frac{5}{12}[/tex]

Step-by-step explanation:

Answer: =5/12

Step-by-step explanation: Hope this help :D

Does the relation {(5,-2), (5,-8), (4,-6), (7,-1)} represent a function?

Answers

Answer:

no, it does not

Step-by-step explanation:

if it was a function, all the x values would've been different, but since 5 is repeated, it is not a function.

Answer: No

Step-by-step explanation:

Find the volume of a cylinder that has a height of 8 inches and a diameter of 14 inches.

Answers

Answer:

[tex]V=1232\ inches^3[/tex]

Step-by-step explanation:

Given that,

The height of a cylinder, h = 8 inches

The diameter of the cylinder, d = 14 inches

Radius, r = 7 inches

We need to find the volume of the cylinder. The formula for the volume of a cylinder is given by :

[tex]V=\pi r^2 h\\\\=\dfrac{22}{7}\times 7^2\times 8\\\\V=1232\ inches^3[/tex]

So, the volume of the cylinder is equal to [tex]1232\ inches^3[/tex].

Which of the following points are solutions to the system of inequalities
shown below?
Check all that apply.
x + y = 4+3
y > 4
O A. (2, -1)
B. (3,6)
C. (2,8)
O D. (1,5)
E. (1,1)
O F. (-1,8)

Answers

D
E
AP3X..
QuIz
anskskskssksksskskwwf

Can you help me with this?

Answers

Answer:

1. Obtuse

2. Right

3.Acute

4.Acute

5.Right

6.obtuse( Not sure about this one)

2+2+2+2+67 I really need help​

Answers

Answer: the answer is 75

Step-by-step explanation:

67 x 4

A number d is greater than −5.

Answers

Answer: d > -5

Step-by-step explanation: Just convert the greater than into a symbol, and you'll be good to go.

Hope this helps!

Help quick!like really quick

Answers

Answer:

2 is 2930in²

Step-by-step explanation:

find the unit rate of 12 dozen ears of corn that cost $36.00

Answers

36.00/12 is 3 dollars for each ear of corn have a nice day (:

What is the approximate area of the circle shown below

Answers

Answer:

43 FT^2

Step-by-step explanation:

3.14159265359 x 3.7^2

Pi times the radius squared

I’m pretty sure the answer is a
Exclamation : Hope this helps

What is the answer to 3/4= 6

Answers

Answer:

False

Step-by-step explanation:

Exposure to ionizing radiation is known to increase the incidence of cancer. One thousand laboratory rats are exposed to identical doses of ionizing radiation, and the incidence of cancer is recorded during subsequent days. The researchers find that the total number of rats that have developed cancer t months after the initial exposure is modeled by for months. Find the rate of growth of the number of cancer cases at the 7th month.

Answers

Missing information :

The model was omitted from the question ; the possible model relating to the question was browsed online and could possibly be :

N(t) = 1.07t^2.3 for 0 ≤ t ≤ 10 months

Answer:

30.9 cases per month

Step-by-step explanation:

Given the model to determine the number of rats that have developed cancer after initial exposure ; N(t) = 1.07t^2.3

N(t) = 1.07t^2.3

Take the first derivative of N with respect to t to obtain the rate of change ;

N'(t) = (1.07)(2.3)t^2.3-1

N'(t) = (1.07)(2.3)t^1.3

The rate of growth of cancer cases at the 7th month can be calculated thus :

t = 7

N'(7) = (1.07)(2.3)t^1.3

N'(7) = 1.07 * 2.3 * 7^1.3

N'(7) = 1.07 * 2.3 * 12.549529

N'(7) = 30.884

The rate of growth of cancer at the 7th month is 30.9 cases per month.

Micah and crystal purchase two movie tickets. Tickets cost $8.50 each. drinks cost $3.50 each, and the boxes of candy cost $3.00 each. use an algebraic expression to desribe how much they spend based on the number of tickets, drinks and boxes of candy they buy

Answers

Answer:

2t+2d+2c=30

2(8.50)+2(3.50)+2(3.00)=$30

Step-by-step explanation:

t= tickets (8.50)

d= drinks (3.50)

c= candy (3.00)

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