Answer the following

Answers

Answer 1

Part a: Inverse of the function- g⁻¹(x) = 3 - 7x.

Part b: Composite function, (g⁻¹o g)(3) = -18.

Part c: The value of h⁻¹(9) = 0.

What is meant as the one-to-one function?A one to one function is a function that maps each element of the range to precisely one element of its domain, ensuring that the outputs never repeat. A normal function can accept two different input values and return the same result, while a one to one function cannot.

Part a: Inverse of the function- g⁻¹(x).

For the given question.

The one-to-one function is given as;

g(x) = (-x + 3)/7

As, it is one-to-one function, its inverse is possible.

Let y = g(x) = (-x + 3)/7

Write function in terms of y.

7y = -x + 3

x = 3 - 7y

Now, replace y with x in the function.

g⁻¹(x) = 3 - 7x

Part b: Composite function, (g⁻¹o g)(3)

First find the composite value of g(3).

g(x) = (-x + 3)/7

Put x = 3

g(3) = (-3 + 3)/7 = 0

Now, put the value of g(3) in g⁻¹(x).

(g⁻¹o g)(3) = 3 - 7x

(g⁻¹o g)(3) = 3 - 7×3

(g⁻¹o g)(3) = -18

Part c: The value of h⁻¹(9).

Check the domain and ranges given for the 'h' function.

h⁻¹(9) has the domain of 0

Thus, h⁻¹(9) = 0.

Thus, the values for the one-to-one function are found.

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Related Questions

PLS HELP ASAP
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2003, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected number of new cases for 2011, rounded to the nearest whole number. (please include work)

Answers

The projected number of newly reported crime cases in the New York county in 2011, found using linear regression is 703 newly reported crime cases

What is a linear regression?

A linear regression models the relationship between a scalar quantity and other explanatory variables, using a linear approach.

The linear regression equation is presented as follows;

y = a + b•x

Where;

[tex] \displaystyle{ b = \frac{ \sum (x - \bar x) \times (y - \bar y)}{ (x - \bar x)^{2} } }[/tex]

[tex] \displaystyle{ a = \frac{ \sum (y ) + b \times \sum (x)}{ n } }[/tex]

[tex] \displaystyle{ \bar x}[/tex] =(0+1+2+3)/4 = 1.5

[tex] \displaystyle{ \bar y}[/tex] =(994+946+928+880)/4 = 937

[tex] \displaystyle{ \sum x}[/tex] =(0+1+2+3) = 6

[tex] \displaystyle{ \sum y}[/tex] =(994+946+928+880) = 3748

n = 4

Using the statistics function of a graphing calculator, under Scatter plot, plot type, we have;

y = 991 - 36•x

Which gives;

b = -36

a = 991

From the given parameters, we have;

x = The number of years since 2003

y = The number of newly reported crime cases

Required;

The number of projected new cases in 2011

Solution;

In 2011, x = 2011 - 2003 = 8

Which gives;

y = 991 - 36×8 = 703

The number of newly reported crime cases in 2011 is 703

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a number divided by 3 decreased by 2 is at most 2

Answers

"A number divided by 3 decreased by 2 is at most" in equation form is 2y/3 -2 ≤ 2

How to convert word problems to equations?

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that: a number divided by 3 decreased by 2 is at most 2

We need to translate the word into an equation:

First, we will assign a letter to the said number. So let the number be y

The number divided by 3: y/3

Then decreased by 2: y/3 -2

And everything is at most 2 (it is less than or equal to 2): y/3 -2 ≤ 2

Therefore, the given word problem can be written as y/3 -2 ≤ 2

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Solve this quadratic equation by factoring.
(x-3)^2 =3(x-3)

Please help me i’m very stuck on this equation

Answers

The expression of the given quadratic equation in factor form is (x - 3)(x - 6) = 0 with a solution of x = 3 or 6.

How to factor quadratic equations?

We are given the quadratic expression;

(x - 3)² = 3(x - 3)

By expansion of the brackets, we have;

x² - 6x + 9 = 3x - 9

x² - 6x + 9 - 3x + 9 = 0

x² - 6x - 3x + 18 = 0

By grouping into brackets we have;

(x² - 6x) - (3x - 18) = 0

By bringing out common factors, we have;

x(x - 6) - 3(x - 6) = 0

Thus, we can write it in factor form as;

(x - 3)(x - 6) = 0

x = 3 or 6

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Hamid has gained weight
He now weighs 88kg,which is 10% higher than his normal weight.
What is his normal weight?

Answers

You can get the answer by reciprocating the multiplying factor of 10%

88*10/11

= 80 kg

Therefore, Hamid's original weight was 80 kgs

Evaluate 2a +7-8a-14+5a

Answers

Answer: -a-7

Step-by-step explanation:

Answer:

−a −7

Step-by-step explanation:

group the 'a's. 2a-8a+5a. It is -a. Next, group the numbers and simplify them. 7-14. It is equal to -7. If you put -a and -7 together, you get "-a-7" as an answer.

solve each of the pairs of simulations equations by elimination
5g+2h=14
3g-4h=-28

Answers

We need to know to solve equations by elimination method to solve the problem. The solution for the given pair of equations is g=0 and h=7.

When we solve a given pair of equations by elimination method, we need to express one of the variables in terms of the other variable and then substitute this value in the other equation to find the value of one of the variables. We use the value of this variable to find the value of the other variable. In this question we have a pair of equations and we need to solve for the variables g and h.

5g+2h=14..(i)

3g-4h=-28..(ii)

From equation (i)

2h=14-5g⇒h=7-5g/2

Substitute this in equation (ii)

3g-4(7-5g/2)=-28

3g-28+10g=-28

13g=0

g=0

Using value of g to find out h

h=7-5g/2=7

Therefore the solution of the given pair of equations is g=0 and h=7.

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PLS HELP ASAP! 20 PT+Brainliest

Answers

Answer:

The graph of a line with 1/2 is only half of 1/4 the line with 4 is greater and way bigger than just half of 1/4.

The vertices of △LMN are L(2, 2), M(5, 3), and N(9, 1). Translate △LMN using the vector 〈−2, 6〉.

Answers

Answer:

(0, 8 ) , (3, 9 ) , (7, 7 )

Step-by-step explanation:

under the translation < - 2, 6 >

subtract 2 from the original x- coordinate

add 6 to the original y- coordinate

then

L (2, 2 ) → L' (2 - 2, 2 + 6 ) → L' (0, 8 )

M (5, 3 ) → M' (5 - 2, 3 + 6 ) → M' (3, 9 )

N (9, 1 ) → N' (9 - 2, 1 + 6 ) → N' (7, 7 )

The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances total $81. How much is each allowance?

You
Friend
how much money do you and how much dose your friend have
.

Answers

Your monthly allowance and your friend's monthly allowance is $45 and $36 respectively.

From the given tape diagram, the ratio of your monthly allowance to your friend's monthly allowance is 5:4.

What is the ratio?

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, 5+4=9

Now, your monthly allowance = 5/9 × 81

= 45

So, your friend's monthly allowance = 81-45 = 36

Therefore, your monthly allowance and your friend's monthly allowance is $45 and $436 respectively.

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What is the x-intercept of a line passing thru points (-3, 5) and (5, 1)?

Answers

The x - intercept of the line passing through the points (-3,5) and (5,1) is

x - intercept:

x intercept means the value of the x coordinate of the point where the graph cuts the x-axis, or x-intercept is the value of the x coordinate of a point where the value of y coordinate value is equal to zero.

Given,

Here we have the points (-3,5) and (5,1).

And we need to find the x intercept of the line passing through the points.

In order to find the x-intercept of a line of the form

y = mx + b,

substitute y = 0.

But the value of m is also unknown.

So, Let the line be

y=mx + b

The line passes through two points (-3,5) and (5,1)

5 = m × (-3) + b

-3m +b = 5 ------------------ (i)

1 = m × (5) + b

5m + b = 1 --------------------(ii)

While we subtracting (ii) from (i) we get,

=> (5m + b) - (-3m + b) = 1 - 5

=> 8m = -4

=> m = -1/2

Substitute the value in (i) we get,

=> -3(-1/2) + b = 5

=> b = 5 - 3/2

=> b = 7/2

Now, the equation of the line is

y = mx + b

when we apply the value then we get,

y = -3/2x + 7/2

When we apply the value of y = 0, then we get,

0 = -3/2x + 7/2

-3/2x = -7/2

x = 7/2 x 2/3

x = 7/3

Therefore, the x intercept is 7/3.

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To order tickets online to a hockey game,
there is a processing fee plus the
cost per ticket. The cost for 5 tickets is $174.45. The cost for 8 tickets is
$271.95. Write and solve a linear equation to find the total cost to order 12 tickets.

Answers

Answer: The total cost to order 12 tickets is $378.05

Step-by-step explanation:

Let y represent the cost for x number of tickets.

Since the cost for 5 tickets is $174.45, it can be represented by the point (5, 174.45).

The cost for 8 tickets is $271.95, it can be represented by the point (8, 271.95).

y = 32.5x - 11.95

The cost for 12 tickets is:

y=32.5(12) - 11.95 = 378.05

Hence the total cost to order 12 tickets is $378.05

HELP!!!
Graph y=1/2x- 3

Answers

Some points you can graph also
(2,-2), (4,1)

Answer: See the graph I attached below.

Step-by-step explanation: Remember to use the slope-intercept form of the equation:

y = mx+b

m = slope

b = y-intercept

Therefore, y=1/2x-3 has a slope of 1/2 and intercepts the y-axis at -3

14.37x14.37 rounded by the nearest mile

Answers

The numbers 14.37x14.37 rounded by the nearest mile is 207 miles.

What is rounding off numbers?

It should be noted that rounding of numbers simply means making the numbers more precise to a certain place values.

In this case, 14.37 × 14.37 will be illustrated as:

= 14.37 × 14.37

= 206.4969

= 207

This gives 207 miles.

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1: En el triángulo rectángulo de la figura, si a =30°, entonces ¿cuál es el valor de P
A) 2
B) 0,5
C) 30°
D) No se puede saber.

Answers

Answer:

can you translate this because I don't understand

Triangle XYZ is shown on the coordinate grid. The coordinates of each vertex of the triangle are integers.

What is the slope of XZ ?

Answers

The slope of line segment XZ in triangle XYZ is: -1/3.

What is the Slope of a Line Segment?

Given a line segment on a coordinate plane, we can find the slope of the line by using two points on the line to find the ratio of change in y / change in x = (y2 - y1)/(x2 - x1).

The coordinates of the two points of line segment XZ in triangle XYZ are:

X(1, 5) = (x1, y1)Z(7, 3) = (x2, y2)

Plug the values into the formula used for finding the slope of a line:

Slope of line segment XZ = change in y / change in x = (5 - 3)/(1 - 7)

Slope of line segment XZ = 2/-6

Slope of line segment XZ = -1/3

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Kylie was out at a restaurant for dinner when the bill came. to find the total plus tip, she multiplied the cost of the meal by 1.2. what percent tip did she leave?

Answers

The percentage of tip that Kylie left is 20%

Finding percentage:

To find the percentage of the number in a given whole number divide the number by the whole number and multiply by 100. To find the percentage of the tip we will calculate the percentage of tips in the total cost.

Here we have,

To find the total plus tip, Kylie multiplied the cost of the meal by 1.2

Let $ x be the cost of the meal

Then total cost plus including tip = x × 1.2 = 1.2x

From the above calculations,

The amount of tip paid by Kylie = 1.2x - x = 0.2x

There percentage of tip = (0.2x)/x × (100) = 20%

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the NBA regulations require the basketball court to be 132 feet long. How many meters is the length if the court?

Answers

Answer:

40.23

Step-by-step explanation:

Can you guys please explain the whole thing of converting I don't know how to do it?

Answers

Answer:

y=6/5x+6

Step-by-step explanation:

so for this you gotta see how far up/down the 2 points are apart as well as how far left/right and should be shown as 'y/x'. this will be your slope. Simplify it as far down as you can but keep it as a fraction.

After that you need to find where it crosses the y axis. lucky for us its stated in the problem. thats the process of finding y= m/x +b

maths helppppppppppp

Answers

Answer:

Acute

Step-by-step explanation:

Answer:

It is Acute.

Step-by-step explanation:

To be right triangle it has to be all perfect sides same length, to be obtuse has to be wider to the sides but this one is acute because it goes inside.

Use the following unit fractions to express 90 miles per hour in feet per second.
5280 ft 60 min
1 mil
1 hr
90 mi
hr
+
ft
sec
, and
60 sec
1 min
(Simplify your answer.)

Answers

Answer:

1235

Step-by-step explanation:

hope

Which ordered pairs are solutions to the inequality 2y−x≤−6?

Select each correct answer.

Responses

(−3, 0)

(6, 1)

(0, −3)

(1, −4)

(2, −2)

Answers

Those ordered pairs that are solutions to the inequality is

(6, 1), (0, −3), (1, −4), (2, −2)

we have 2y−x≤−6

we know that

if a ordered pair is a solution of the inequality then, the ordered pair must satisfy the inequality

we will proceed to verify each case to determine the solution of the problem

case A)(-3, 0)