Find: f^-1(x)=2x/2+3x make sure it is 1-1, if so find the inverse and verify by composition in both directions
Answers
The function is one-one can be dtermined by using horizontal line test. If horizontal line on the graph of function intersect the function more than once then such function is not one-one. The graph of function is,
Since horizontal lines intersect the curve of function only once so function is one-one.
Determine the inverse of the function.
[tex]y=\frac{2x}{2+3x}[/tex]Interchange x with y and y with x and simplify the obtain equation for x.
[tex]\begin{gathered} y=\frac{2x}{2+3x} \\ y\cdot(2+3x)=2x \\ 2y+3xy=2x \\ 3xy-2x=-2y \\ x(3y-2)=-2y \\ x=-\frac{2y}{3y-2} \end{gathered}[/tex]Substitute y by x for the inverse of function.
[tex]f(x)=\frac{-2x}{3x-2}[/tex]So inverse of the function is -2x/(3x - 2).
So functions f and g are inverse of each other if,
[tex]f(g(x))=g(f(x))=x[/tex]Check the obtained inverse function by composition.
[tex]\begin{gathered} f^{-1}(-\frac{2x}{3x-2})=\frac{2\cdot(-\frac{2x}{3x-2})}{2+3\cdot(-\frac{2x}{3x-2})} \\ =\frac{-\frac{4x}{3x-2}}{\frac{6x-4-6x}{3x-2}} \\ =-\frac{4x}{-4} \\ =x \end{gathered}[/tex][tex]undefined[/tex]
Related Questions
use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. If two orders are selected, find the probability that they are both accurate. Complete parts (a) and (b) below.
a. Assume that the selections are made with replacement. Are the events independent?
The probability is __. The events __ (are, are not) independent.
(Do not round until the final answer. Round to four decimal places as needed.)
Answers
Answer:
a. If the selection is made with replacement, they are NOT independent because they affect each other.
b. The probability of selecting TWO accurate orders is .7157 and the events ARE independent.
Step-by-step explanation:
Add the accurate orders:
315+273+248+125=961
Add the inaccurate orders:
38+56+37+17=148
148/961=0.1540 probability of getting ONE inaccurate order
1.0-0.1540=0.846 probability of selecting ONE accurate order
0.846 * 0.846 = 0.7157 the probability of selecting TWO accurate orders
Therefore, the probability is .7157 and the events ARE independent.
he graphs of the functions and are shown below. For each graph, find the absolute maximum and absolute minimum.
Answers
From the given graph
The graph of g has an arrow with the left end it goes up, then
The absolute maximum of g is NONE
The graph of g has a minimum point (4, -4), then
The absolute minimum is -4
The graph of h has a maximum point (-4, 4), then
The absolute maximum is 4
The graph of h has a minimum point (-1, -4), then
The absolute minimum is -4
You are the owner of Caché, a chain of women's clothing boutiques. Your state has a sales tax of 7%, and your city has an additional sales tax of 1.5%. Each quarter you are responsible for making these tax deposits to the city and state. Last quarter your stores had total revenue, including sales tax, of $271,250.
Answers
(a) 250000 of this revenue was sales and $11250 much was sales tax. (b) $11250 of sales tax should be sent to the city and $3750 sales tax should be sent to the state.
Let us assume that the total sales are $X.
According to the given situation, 7% is the sales tax and an additional state sales tax of 1.5% will be charges on the sales.
The total revenue including sales tax is $271250.
(a) Total revenue = sales + total sales tax
So, we can write,
X + X(7+1.5)% = 271250
Solving further,
X + X(8.5%) = 271250
X + 8.5X/100 = 271250
108.5X = 271250×100
X = 250000
Total sales is $250000.
Total sales tax is $(2710250-250000)
Total sales tax is $21250.
(b) Total sales is $250000.
Tax charges by city is 7%.
Using percentage formula,
Percentage of tax = Total tax amount/Total sales amount × 100
Putting all the values,
7 = Total tax amount/250000 × 100
Total tax amount = 7 × 2500
Total tax amount = 17500 dollars.
Total amount to be sent to the city is 175000$.
(c) Total sales is $250000.
Tax charges by city is 1.5%.
Using percentage formula,
Percentage of tax = Total tax amount/Total sales amount × 100
Putting all the values,
1.5 = Total tax amount/250000 × 100
Total tax amount = 1.5 × 2500
Total tax amount = 3750 dollars.
Total amount to be sent to the city is 175000$.
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i can provide a better picture if needed but i only need help with b
Answers
Taking a look at the graph, we can notice that point (7000,2875.99) is highlighted.
Using this point, we can conclude that the cost of talking 7000 minutes is $2875.99
3 sisters age combined are 57. Jenny is 6 years
older then Lynn. Kim is 5 less then twice the age of
Lynn age. What are each sisters ages
Answers
Answer:
Step-by-step explanation:
Jenny is 20 years old
Lynn is 14 years old
Kim is 23 years old
Select the correct answer.
Which expression is equivalent to ³+2+3 if no denominator equals zero?
=+1
OA.
3
B.
+3
OC. 2-3
OD. +
Answers
The second expression 1/(x^2 - 4x + 3) is equivalent to the given expression.
What are the equivalent expression?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Consider the given expression,
((x + 3) / (x^2 - 2x - 3)) / ((x^2 + 2x -3)/ (x + 1))
We can write the expression as,
((x + 3) / (x^2 - 2x - 3)) x ((x + 1) / (x^2 + 2x -3))
Rewrite the equation x^2 - 2x - 3 and x^2 + 2x -3 as,
x^2 - 2x - 3 = x^2 - 3x + x - 3 = (x - 3)(x + 1)
x^2 + 2x - 3 = x^2 + 3x - x - 3 = (x + 3)(x - 1)
plug these values in the above expression, we get
((x + 3) / ((x - 3)(x + 1)) x ((x + 1) / ((x + 3)(x - 1))
After solving this, we get
1 / ((x - 3)(x - 1) = 1 / (x^2 - 4x + 3)
Therefore, the second expression is equivalent to the given expression.
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Find g(x), where g(x) is the translation 4 units down of f(x)=x.
Write your answer in the form mx+b, where m and b are integers.
(Will mark best answer brainliest)
Answers
Answer:
g(x) + 4 = x
g(x) = x - 4 which is probably the answer you should submit.
Step-by-step explanation:
Givens
f(x) = x
g(x) +4 = f(x)
Comment
f(x) and g(x) are forms of y or z. What they mean is that whatever x is on the left, it will be make the same on the right. It is just a short hand to help you in defining the y value.
If you want to move down, The y value is the one to notice. Notice that it is not intuitive. If you want to go down the sign on y + 4 = x is the equation you use. It is the exact opposite of what you think it should be. The graph below should help you.
The red line is f(x) = x
The blue line is g(x) + 4 = x.
The blue line can be written as g(x) = x - 4 which would be more inetuitive.
The projected profit (in thousands of dollars) of a new technology company in year t can be modeled by the polynomial 2t2 - 9t - 18
When the company will break even (have zero profit)? Show all work necessary to justify your answer.
The projected profit (in thousands of dollars) in year t of a newly developed line of business can be modeled by the monomial t3 . Write a polynomial that models the company’s total profit including this new line of business.
How many years sooner will the company break even with the new line of business? Show all work necessary to justify your answer.
Answers
a. The company will break even in 6 years
b. The total profit with the newly developed line of business is:
[tex]t^3+2t^2-9t-18[/tex]c. The company will break even 3 years sooner
Explanation:The projected profit is given as:
[tex]2t^2-9t-18[/tex]a. The company will break even when the profit is zero. That is;
[tex]\begin{gathered} 2t^2-9t-18=0 \\ \\ (2t+3)(t-6)=0 \\ 2t+3=0 \\ \Rightarrow t=-\frac{3}{2} \\ \\ t-6=0 \\ t=6 \end{gathered}[/tex]6 is the realistic number of years (As we cannot have -3/2 years).
We conclude that they will break even in 6 years
b. The projected profit of a newly developed line of business is:
[tex]t^3[/tex]The total profit is now;
[tex]t^3+2t^2-9t-18[/tex]The company will break even with this new line of business as follows:
[tex]\begin{gathered} t^3+2t^2-9t-18=0 \\ (t+2)(t+3)(t-3) \\ t+2=0 \\ \Rightarrow t=-2 \\ t+3=0 \\ \Rightarrow t=-3 \\ t-3=0 \\ \Rightarrow t=3 \end{gathered}[/tex]We choose t = 3 (because we cannot have -2 years or -3 years)
The difference between this and the previous time is 6 - 3 = 3 years
The company will break even 3 years sooner
Write the correct equation for the following statement.
You decide to rent a limo for prom. The rate is $175 plus $5 per mile
traveled. Write an equation to calculate your total cost (c) at the end of the evening for a given number of miles (m).
If you travel 45 miles what will be your total bill at the end
of the evening?
Answers
Answer:
Step-by-step explanation:
If I did the math right! The bill should be $400.00
How I did it, was I did 175+5x45.
seeing, it is $5 per mile! And the total miles you got was 45.
If I missed something, please let me know
Many graduate schools require applicants to take a certain test. Those taking the test receive three scores: a verbal reasoning score, a quantitative reasoning score, and an analyticalwriting score. In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.3 points, and the average verbal reasoning score exceeded theanalytical writing score by 150.5 points. The sum of the three average scores was 305.9. What was the average score for each category?The average verbal reasoning score was (Type an integer or a decimal.)The average quantitative reasoning score was (Type an integer or a decimal.)The average analytical writing score was (Type an integer or a decimal.)
Answers
Many graduate schools require applicants to take a certain test. Those taking the test receive three scores:
a verbal reasoning score,
a quantitative reasoning score,
an analytical writing score.
Let average verbal reasoning score represent by v
Let average quantitative reasoning score represent by q
Let average analytical writing score represent by a
In 2013, the average quantitative reasoning score exceeded the average verbal reasoning score by 1.3 points
i.e.,
Average quantitative reasoning score - average verbal reasoning = 1.3
q - v = 1.3 ...(1)
The average verbal reasoning score exceeded the analytical writing score by 150.5 points.
i.e.,
Average Reasoning score - average analytical writing = 150.5
v - a = 150.5 ...(2)
The sum of the three average scores was 305.9.
i.e.,
v + q + a = 305.9 ...(3)
Simplify the equation (1), (2) and (3) to get the value of q,v and a;
Add equation (1) and (2)
(q-v) + (v-a) = 1.3 + 150.5
q + a = 151.8 ....(4)
Substitute the value of (q+a=151.8) in the equation (3);
v + q + a = 305.9
v + 151.8 = 305.9
v = 305.9 - 151.8
v = 154.1
Substitute the value of v = 154.1 in the equation (2);
v - a = 150.5
154.1 -a = 150.5
a = 154.1 - 150.5
a = 3.6
Now, substitute the value of a = 3.6 in the equation (4)
q + a = 151.8
q + 3.6 = 151.8
q = 151.8 - 3.6
q = 148.2
Answer :
The average verbal reasoning score was 154.1
The average quantitative reasoning score was 148.2
The average analytical writing score was 3.6
please help with this practice question
Answers
Not 100% sure though
Given this equation, what would the restriction be?X+6/x= -7
Answers
Given:
The equation is:
[tex]x+\frac{6}{x}=-7[/tex]Find-:
Restrictions for this equation
Explanation:
The equation is:
[tex]\begin{gathered} x+\frac{6}{x}=-7 \\ \\ \frac{x^2+6}{x}=-7 \end{gathered}[/tex]The denominator is not equal to zero. If the denominator is zero, then the function is undefined.
Then the restriction is:
[tex]x\ne0[/tex]For the function value of x is:
[tex]\begin{gathered} \frac{x^2+6}{x}=-7 \\ \\ x^2+6=-7x \\ \\ x^2+7x+6=0 \\ \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} x^2+6x+x+6=0 \\ \\ x(x+6)+1(x+6)=0 \\ \\ (x+6)(x+1)=0 \\ \\ x=-6\text{ and }x=-1 \end{gathered}[/tex]So above function value of x is possible only -6 and -1 then the restriction value is all real numbers except only -6 and -1
[tex][/tex]g(x)=-3x-1 What is g(10
Answers
A function is a relation that gives one input for every one output thus the value of g(10) is -31.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given function,
g(x) = -3x - 1
The value of the function at x = 10
g(10) = -3(10) - 1
g(10) = -30 - 1 = -31
Hence "A function is a relation that gives one input for every one output thus the value of g(10) is -31".
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tammy deposits $8,000 into an account that pays simple interest at a rate of 3% per year how much interest will she be paid in the first 4 years
Answers
Define a variable, set up an equation, then solve. the sum of two numbers 146. the larger number is 16 less than five times the smaller number. find both numbers.
Answers
The smaller number = 27
The larger number = 119
Explanations:Let the smaller number be x
Let the larger number be y
The sum of the two numbers is 146
x + y = 146..............(1)
The larger number is 16 less than five times the smaller number
y = 5x - 16.............(2)
Substitute equation (2) into equation (1)
x + (5x - 16) = 146
x + 5x - 16 = 146
6x = 146 + 16
6x = 162
x = 162/6
x = 27
Substitute the value of x into equation (2)
y = 5(27) - 16
y = 135 - 16
y = 119
The smaller number = 27
The larger number = 119
What is the solution to the division problem below? (You can use long divisionor synthetic division.)2x3 - 4x2 – 3x-9X-3A. 2x2 + 3x + 3B. 2x2 + x + 3C. 2x2 + 4x + 3O D. 2x2 + 2x+3
Answers
The answer for this process of long division is, therefore:
[tex]q=2x^2+2x+3[/tex]To find the result for this long division, we needed to divide the first term of the polynomial by the x in the divisor. Then, if we see the first graph, we have:
[tex]\frac{2x^3}{x}=2x^2[/tex]Then, we need to multiply this term by the divisor (x - 3), and then, subtract the result from the first two terms of the dividend. We can see as follows:
I need help with my math
Answers
Please provide the question.
We are asked to select the mathematical expressions that represent 40% of 84
We then recall that the mathematical form of 40% is in fact 40 / 100 = 0.4
Then, 40% of 84 can be written in math terms as:
40/100 times 84 = 40/100 * 84
or also
0.4 times 84 = 0.4 * 84
Therefore there are TWO options we can select in the list of possible answers:
Answer C and answer E
Which of the following boxes should replace the question mark (?) to complete the pattern?
Answers
The most appropriate choice for pattern will be given by
Option E is the correct option
What is pattern?
Repeated arrangement of number or shape is called pattern.
Here,
Let the boxes be counted row wise
The question is all about filling all the blank boxes with orange colour.
Let the pattern be solved column wise
In the first column,
In first figure
The 2nd, 3rd and 4th boxes are filled with orange colour
Then in the second figure 5th box is filled with orange colour
To complete filling all the boxes with orange colour, 1st, 6th, 7th, 8th and 9th boxes are left. That is shown in the third figure.
In the third column
In first figure
The 5th, 6th and 9th boxes are filled with orange colour
Then in the second figure
1st, 2nd, 4th, 7th and 8th boxes are filled with orange colour
To complete filling all the boxes with orange colour, only the 3rd box is left
That is shown in third figure
Now, in the second column,
In the first figure,
1st, 7th and 8th boxes are filled with orange colour.
Then in the second figure 3rd, 6th and 9th are filled with orange colour
To complete filling all the boxes with orange colour, 2nd, 4th and 5th boxes are left.
That is shown in option E
So option E is correct
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Patrick is a mountain climber. One morning, he drove to the base of a mountain whichwas at an elevation of 900 meters. While he climbed, he gained an average of 45 metersof elevation per hour. What is the slope and y-intercept of the function representingPatrick's elevation during his climb?
Answers
45 represents the slope while -900 is the y-intercept of the function
Here, we want to write the slope and y-intercept of the function that represents Patrick's elevation during his climbing
From the question, we are told that he averaged an elevation of 45 meters per hour
What the slope basically does is to measure a rate of change. As we can see from here, the change represents a rate and thus, we have this as our slope
To get the y-intercept of the function, we can see this as a distance of -900 meters
The reason for this is that we can see the summit of the mountain as 0 m
So we can represent the equation as;
[tex]y\text{ = 45x-900}[/tex]Hi, I was absent while my class learned this and I am unsure of how to solve for either. Any help/ explanation would be appreciated. Thanks!
Answers
Given: The figure shown
To Determine: The value of EF
Solution
Using intersecting chord theorem that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
Applying the theorem to the given would give us
[tex]CD\times DP=EF\times FP[/tex]Therefore
[tex]\begin{gathered} 11cm\times9cm=EF\times10cm \\ 99cm^2=EF\times10cm \\ EF=\frac{99cm^2}{10cm} \\ EF=9.9cm \end{gathered}[/tex]2. Let us label the the image given
Compare 2x + 8 > 18 and 2c +8 < 18.
Answers
The given inequalities are :
2x + 8 > 18
2c + 8 < 18
Inequality 1 : 2x + 8 > 18
Simplify
Subtract 8 from both side :
2x + 8 - 8> 18 - 8
2x > 10
Divide both side by 2
x > 5
Inequality : 2c + 8 < 18
2c + 8 < 18
Subtract 8 from both side:
2c + 8 - 8 < 18 - 8
2c < 10
Divide both side by 2:
2c/2 < 10/2
c < 5
So, the solution is x > 5 and c < 5
So, equation will be : c < x < 5
On a public transportation map, two stations are 9 centimeters apart, whereas in real life thedistance between them is 3 kilometers. What is the scale of the map?Write your answer in simplest form using whole numbers.centimeters =kilometers
Answers
Given:
The distance between two stations in map, D= 9cm.
The distance between two stations in real life, d=3 km.
Now, to find the scale of the map take the ratio of D/d .
[tex]\frac{d}{D}=\frac{3\operatorname{km}}{9\text{ cm}}=\frac{1\operatorname{km}}{3\text{ cm}}=\frac{1}{3}\frac{km}{\operatorname{cm}}[/tex]So, the scale of the map is 1 km=3 cm.
The function D = 25 + 0.3x represents the daily rental charge D (in dollars) for x miles driven. Is the domain discrete or continuous?
Answers
Hello!
First, let me explain the difference between discrete and continuous.
Discrete: only some numbers of the interval are on the input. For example, in the interval 1 - 10, consider only the integers.
Continuous: all the numbers of the interval are on the input. For example: in the interval 1 - 10, all values are considered (integers and decimals).
Knowing it, let's analyze your exercise:
The function D = 25 + 0.3x represents the daily rental charge D (in dollars) for x miles driven.
We can represent miles as integers and also decimals, right?
• 2 miles
,• 5.750 miles
So, it means that all values can be considered.
Answer:So, this is a continuous domain.
Jessie has 5 dogs. 2 of them are male and 3 of them are female. What percent of the dogs are male?
Answers
Given
Jessie has 5 dogs
2 are male
3 are female
Procedure
What percent of the dogs are male?
Male dogs
[tex]\frac{2\text{males}}{5\text{ total}}=0.4=40\text{ \%}[/tex]40 % of dogs are male
write in slope-intercept form an equation of the line that passes thorugh the given points.(1,2), ( -2, -1)
Answers
Determine the equation of line passing through two points.
[tex]\begin{gathered} y-2=\frac{-1-2}{-2-1}(x-1) \\ y-2=-\frac{3}{-3}(x-1) \\ y-2=x-1 \\ y=x+1 \end{gathered}[/tex]So equation of line is,
[tex]y=x+1[/tex]Can someone help me?? I just need 2 and 3
Answers
The current area of Mr. Milstein's kitchen table is:
[tex]=17\frac{1}{2}\text{ square fe}e\text{t}[/tex]The new width of Mr. Milstein's kitchen table = 5 feet
The area of the new kitchen table if the length is l is given by
[tex]\text{ Area (A) = length x width = 5l}[/tex]Note that the area of the proposed kitchen table should be larger than the current one.
[tex]\begin{gathered} \text{ The current area = }17\frac{1}{2}\text{ square fe}e\text{t} \\ \text{ The new area = 5 x l = 5l} \\ \text{ Therefore,} \\ \text{ proposed area > new area} \\ \text{ 5l >}17\frac{1}{2}\text{ square fe}e\text{t} \end{gathered}[/tex]Therefore,
[tex]\text{ 5l >}17\frac{1}{2}\text{ square fe}e\text{t can be used to get the length of the new table}[/tex]The correct option is F
A vehicle travels 426 kilometers in 6 hours. Find the unit rate
Kilometers per hour
Answers
Speed = distance/time (s = d/t)
Distance: 426 km
Time: 6 hours
Plug these values into the format S = d/t
S = 426 km/6 hours
S = 71 kph
The vehicle traveled 71 kilometers per hour.
helppppppppppp meeeeeeeeeeeeeee
Answers
Answer:
A. f(-2) = 13
B. f(0) = 1
C. f(7) = -41
Step-by-step explanation:
f(x) = 1 - 6x
A.
f(-2) = 1 - 6(-2)
f(-2) = 1 + 12
f(-2) = 13
B.
f(0) = 1 - 6(0)
f(0) = 1
C.
f(7) = 1 - 6(7)
f(7) = 1 - 6(7
f(7) = -41
I hope this helps!
PLEASEE HELP THIS IS DUE 2DAY!!!!!!
Create and solve a word problem using the equation 2×+12>2(×+6).include steps and strategies on how to solve the word problem
Answers
2x+12>2x+12
-2x-12 -2x -12
That would be infinite
The least positive number x for which cos x = 0 is "blank"
enter your response here.
(Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) TUSM!!!!!
Answers
The least positive number x for which cos x = 0 is 1.
The given trigonometric equation is cos x=0.
What is the trigonometric equation?A trigonometric equation is one that involves one or more of the six functions sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.
Now, cos x = 0
So, [tex]x=cos^{-1}(0)[/tex]
⇒ x = 1
Therefore, the least positive number x for which cos x = 0 is 1.
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