Which of the following pairs of functions are inverses of each
other?

Answers

Answer 1

Answer: C

Step-by-step explanation:

For this problem, let's find the inverse for all f(x) and see which pairs with the g(x). To find the inverse, you replace the x with y and y with x. Then you solve for y.

A. Incorrect

[tex]y=\frac{x-8}{4} +9[/tex] [replace x with y and y with x]

[tex]x=\frac{y-8}{4} +9[/tex] [subtract both sides by 9]

[tex]x-9=\frac{y-8}{4}[/tex] [multiply both sides by 4]

[tex]4(x-9)=y-8[/tex] [add both sides by 8]

[tex]4(x-9)+8=y[/tex]

This does not match g(x), therefore, they are not inverses of each other.

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B. Incorrect

[tex]y=4(x-12)+2[/tex] [replace x with y and y with x]

[tex]x=4(y-12)+2[/tex] [subtract both sides by 2]

[tex]x-2=4(y-12)[/tex] [divide both sides by 4]

[tex]\frac{x-2}{4} =y-12[/tex] [add both sides by 12]

[tex]\frac{x-2}{4} +12=y[/tex]

This does not match g(x), therefore, they are not inverses of each other.

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C. Correct

[tex]y=3(\frac{x}{2})-4[/tex] [replace x with y and y with x]

[tex]x=3(\frac{y}{2} )-4[/tex] [add both sides by 4]

[tex]x+4=3(\frac{y}{2} )[/tex] [divide both sides by 3]

[tex]\frac{x+4}{3} =\frac{y}{2}[/tex] [multiply both sides by 2]

[tex]\frac{2(x+4)}{3} =y[/tex]

This matches g(x), therefore, they are inverses of each other.

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D. Incorrect

[tex]y=3(\frac{2}{x} )-10[/tex] [replace x with y and y with x]

[tex]x=3(\frac{2}{y} )-10[/tex] [add both sides by 10]

[tex]x+10=3(\frac{2}{y} )[/tex] [divide both sides by 3]

[tex]\frac{x+10}{3} =\frac{2}{y}[/tex] [multiply both sides by y]

[tex](y)(\frac{x+10}{3} )=2[/tex] [multiply both sides by [tex]\frac{3}{x+10}[/tex] or divide by [tex]\frac{x+10}{3}[/tex]]

[tex]y=\frac{6}{x+10}[/tex]

This does not match g(x), therefore, they are not inverses of each other.

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After going through each problem, we found that the correct answer is C.

Related Questions

a student randomly picked three different points on a line, and then noticed that all three points were also on on the same circle

Answers

Answer:

C)It is impossible.

Step-by-step explanation:

According to the situation, the three different points should not be on the same line as it is possible that the circle would possibly a radius of infinite which reflects the impossible as it is nothing but infinite true. So, it is impossible that three different picked points on a line could be on a circle.

There is no straight section across a curvature of a circle as the points cannot be the same distance from the middle as it is the definition of a circle.

So, the correct answer is C

The product of sin 30 and sin 60 is same as the product of

Answers

Step-by-step explanation:

Sin(30)=0.5

Sin(60)=0.866

Sin(30)*sin(60)=0.433

In a study of red/green color blindness. 1000 men and 2800 women are randomly selected and tested Among the men. 85 have red/green color blindness. Among the women, 6 have red/green color blindness.1. Test the claim that men have a higher rate of red/green color blindness- The test statistic is _____- The P-Value is _____- Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women using the 0.05% significance level?A. Yes.B. No.2. Construct the 95% confidence interval for the difference between the color blindness rates of men and women_____ <(P1âP2)<_____

Answers

Answer:

1. Yes, there is sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women.

2. The 95% confidence interval for the difference between the color blindness rates of men and women is [0.0656, 0.1004].

Step-by-step explanation:

We are given that in a study of red/green color blindness. 1000 men and 2800 women are randomly selected and tested

Among the men, 85 have red/green color blindness. Among the women, 6 have red/green color blindness.

Let [tex]p_1[/tex] = population proportion of men having red/green color blindness.

[tex]p_2[/tex] = population proportion of women having red/green color blindness.

So, Null Hypothesis, : {means that men have a lesser or equal rate of red/green color blindness than women}

Alternate Hypothesis, : {means that men have a higher rate of red/green color blindness than women}

(1) The test statistics that will be used here is Two-sample z-test statistics for proportions;

T.S. = ~

N(0,1)

where, = sample proportion of men having red/green color blindness = = 0.085

[tex]\hat p_2[/tex] = sample proportion of women having red/green color blindness = [tex]\frac{6}{2800}[/tex] = 0.002

[tex]n_1[/tex] = sample of men = 1000

[tex]n_2[/tex] = sample of women = 2800

So, the test statistics = [tex]\frac{(0.085-0.002)-(0)}{\sqrt{\frac{0.085(1-0.085)}{1000}+\frac{0.002(1-0.002)}{2800} } }[/tex]

= 9.37

The value of z-test statistics is 9.37.

Also, the P-value of the test statistics is given by;

P-value = P(Z > 9.37) = Less than 0.0001

Since the P-value of our test statistics is less than the level of significance as 0.0001 < 0.05%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we support the claim that men have a higher rate of red/green color blindness than women.

(2) The 95% confidence interval for the difference between the color blindness rates of men and women ([tex]p_1-p_2[/tex]) is given by;

95% C.I. for ([tex]p_1-p_2[/tex]) = [tex](\hat p_1-\hat p_2) \pm Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }[/tex]

= [tex](0.085-0.002) \pm (1.96 \times \sqrt{\frac{0.085(1-0.085)}{1000}+\frac{0.002(1- 0.002)}{2800} } )[/tex]

= [tex]0.083 \pm0.0174[/tex]

= [0.0656, 0.1004]

Here, the crtical value of z at 2.5% level of significance is 1.96.

Hence, the 95% confidence interval for the difference between the color blindness rates of men and women is [0.0656, 0.1004].

pt 2 5-7 please helpp

Answers

Answer:

x = 12

Step-by-step explanation:

__9x__ = __108___

9 9

x = 12

Hi there! Hopefully this helps!

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Answer: x = 12.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]9x = 108[/tex]

Divide both sides by 9.

[tex]\frac{108}{9}[/tex]

Divide 108 by 9 to get, you guessed it, 12!

This visual representation shows the sets of real numbers.
Which statement is true regarding the number sets?
Whole numbers and natural numbers have no
numbers in common.
Some natural numbers are also whole numbers, but
not all natural numbers are whole numbers.
All whole numbers are also natural numbers.
All natural numbers are also whole numbers.

Answers

Answer:

All natural numbers are also whole numbers.

Step-by-step explanation:

Natural numbers are called counting numbers. They are numbers you can count. Although, Zero is not among them. Neither are negative numbers. Succinctly put, Natural numbers are numbers you can count with the exception of negative numbers and Zero.

Whole numbers are an extension of natural numbers. Unlike Natural numbers although, whole numbers contain Zero. Yet, like natural numbers, that do not contain negative numbers. As a result, we can call them counting numbers that includes Zero.

Now from the above definitions, we can see that

1, whole numbers and natural numbers have many numbers in common. So then, 1 is wrong.

2, all natural numbers are whole numbers, not some. So then, 2 is wrong

3, all whole numbers are not natural numbers, because Zero is a whole number, yet, it's not a natural number.

4, all natural numbers are whole numbers, and this is our answer.

this is rlly easy im just hella lazy and i dont wanna answer it- pls help tyyy

Answers

Answer:

Step-by-step explanation:

the other ones are adding and the 3 is obviously being subtracted.

The answer is D since it’s a -3 it means it’s subtracting not adding

4) A bay contains 18 balls out of which ac balls
are white :
one ball is drawn at random
what is the probability that it is white
ii) at two more white balls are put in the
bag
the probability of craving a white ball
& times than that it was before. Find a

Answers

Answer:

find a what?because it dont tell us what to find

Write the set of all real numbers greater than 19 and less than 32 in set-builder notation.
The set-builder notation is {x|

Answers

Answer: {xI x ∈ R, 19 < x < 32}

Step-by-step explanation:

This notation is:

{xI condition1, condition2, ...}

The first condition is:

From what set we take the values of x?

From the set of real numbers.

x ∈ R

The other conditions are the limitations that we have for x, in this case:

19 < x < 32

Then we can write this as:

{xI x ∈ R, 19 < x < 32}

Three people of kaui Island are named Alice, Bob and Carol. At least one of them is a Knight and at least one is a Knave. Exactly one of them has a prize.
They made the following statements:
Alice: Bob doesn’t have the prize
Bob: I don’t have the prize
Carol: I have the prize
Using logic & truth table find that Who has the prize?

Answers

Answer: Alice has the prize

Step-by-step explanation:

[tex]\boxed{\begin{array}{c|c|c||l}\underline{Alice}&\underline{Bob}&\underline{Carol}&\underline{Prize}\\T&T&F&\text{Alice}\\T&F&F&\text{no possible answer}\\T&F&T&\text{no possible answer}\\F&T&T&\text{no possible answer}\\F&F&T&\text{no possible answer}\\F&T&F&\text{no possible answer}\end{array}}[/tex]

Line 1:

Alice: Bob doesn’t have the prize (T) ... either Alice or Carol

Bob: I don’t have the prize (T) ... either Alice or Carol

Carol: I have the prize (F) ... either Alice or Bob

Alice is true for all of them!

Line 2:

Alice: Bob doesn’t have the prize (T) ... either Alice or Carol

Bob: I don’t have the prize (F) ... Bob

Carol: I have the prize (F) ... either Alice or Bob