Mathematics High School

What is the inverse of the function f(x) = 2x + 1?

h(x) = 1/2 x – 1/2
h(x) = 1/2 x + 1/2
h(x) = 1/2 x – 2
h(x) = 1/2 x + 2
What is the exact answer?

Answers

Answer 1

Answer:

[tex]h(x)=\frac{x}{2}-\frac{1}{2}[/tex]

Step-by-step explanation:

Hello

Step1

Let f(x)=y

f(x) = 2x + 1

(1)y= 2x + 1  

to find the inverse of f(x)

Replace every x with a y and replace every y with an x

y= 2x + 1

replacing  

x=2y+1

Step 2

Now solve the equation for y

x=2y+1

subtract 1 on both sides

x-1=2y+1-1

x-1=2y

divide boths dies by 2

(x-1)/2=2y/y

[tex]\frac{x-1}{2} =\frac{2y}{2} \\y=\frac{x-1}{2}[/tex]

let this last equation h(x)= inverse of f(x)

[tex]h(x)=\frac{x-1}{2}\\h(x)=\frac{x}{2}-\frac{1}{2}[/tex]

Have a great day

Related Questions

The perimeter of dawna's new flat screen television is 70 inches. the ration from length to width is 4:3. write and solve an algebraic equation to determine the dimensions of the television

Answers

I hope this helps you

The number 72 is between what two perfect squares? Enter a numerical answer only.

Answers

Well a perfect square looks like this:

6 x 6
2 x 2

So the number 72 is between the PRODUCT of two perfect squares such as those.

One product has to be above 72, and the other below it.

So lets multiply.

8 x 8 = 64
9 x 9 = 81

Oh look at that, 72 is between 64 and 81.



64=8^2
81 = 9^2

72 is between what two perfect squares 64=8^2 and 81 = 9^2

What is the circumference of a circle whose area is 121 pi square meters?

Answers

I hope this helps you


Find the area of a regular hexagon with the given measurement.

2 sqrt3 apothem

A =

...?

Answers

There are 6 sides to a hexagon. 360/6 = 60. So each angle going out to each side measures 60 degrees. We can split one side in half to create a right triangle which has a 30 degree angle. The adjacent is the apothem. We want to find the opposite of this triangle because it will give us half the length of the side of the hexagon. So we can use tangent.

[tex]\sf tan(x^o)=\dfrac{Opposite}{Adjacent}[/tex]

[tex]\sf tan(30^o)=\dfrac{x}{2\sqrt{\sf 3}}[/tex]

We know that [tex]\sf tan(30^o)=\dfrac{1}{\sqrt{\sf 3}}[/tex]:

[tex]\sf \dfrac{1}{\sqrt{\sf 3}}=\dfrac{x}{2\sqrt{\sf 3}}[/tex]

Multiply [tex]\sf 2\sqrt{\sf 3}[/tex] to both sides:

[tex]\sf x=\dfrac{2\sqrt{\sf 3}}{\sqrt{\sf 3}}[/tex]

Simplify:

[tex]\sf x=2[/tex]

So half the side length of the hexagon is 2. That means the entire side length is 2 * 2 = 4.

Now use the formula:

[tex]\sf A=\dfrac{1}{2}ap[/tex]

This is used to calculate the area of any regular polygon. Where 'a' is the apothem and 'p' is the perimeter. The side length is 4, a hexagon has 6 sides, so the perimeter is 6 * 4 = 24. Plug in what we know:

[tex]\sf A=\dfrac{1}{2}(2\sqrt{\sf 3})(24)[/tex]

Simplify:

[tex]\boxed{\sf A=24\sqrt{\sf 3}}[/tex]

Answer:

41.57 unit²

Step-by-step explanation:

We know,

Area of a regular hexagon = [tex]3\times (sidelength)\times (apothem)[/tex].

The length of the apothem = [tex]2\sqrt{3}[/tex] units.

Since, we know, 'a regular hexagon splits into 6 identical equilateral triangles'.

As, the apothem of the regular hexagon = height of the equilateral triangle

So, height of the equilateral triangle = [tex]2\sqrt{3}[/tex] units.

As, in the equilateral triangle, 'One of the side length is the S, other will be [tex]\frac{S}{2}[/tex] and height is [tex]2\sqrt{3}[/tex] units'.

So, using Pythagoras Theorem, we have,

[tex]hypotenuse^{2}=perpendicular^{2}+base^{2}[/tex]

i.e. [tex]S^{2}=(\frac{S}{2})^{2}+(2\sqrt{3})^{2}[/tex]

i.e. [tex]S^{2}=\frac{S^2}{4}+12[/tex]

i.e. [tex]S^{2}-\frac{S^2}{4}=12[/tex]

i.e. [tex]\frac{3S^2}{4}=12[/tex]

i.e. [tex3S^2=48[/tex]

i.e. [texS^2=16[/tex]

i.e. S= 4 units

That is, the side length of the hexagon = 4 units.

Thus, the area of the hexagon is given by,

Area of a regular hexagon = [tex]3\times (4)\times (2sqrt{3})[/tex]

i.e. Area of a regular hexagon = [tex]12\times (2sqrt{3})[/tex]

i.e. Area of a regular hexagon = [tex]24sqrt{3}[/tex]

i.e. Area of a regular hexagon = 41.57 unit²

Hence, the area of the regular hexagon is 41.57 unit².

Simplify by combining like terms step by step
- (3x - 4y) + x

Solve each formula for the indicated variable. step by step
h = vt -5t^2 , for v

Answers

I hope this helps you
- (3x - 4y) + x = (distribute through the parenthesis)
-3x + 4y + x.....combine like terms
-2x + 4y

h = vt - 5t^2....add 5t^2 to both sides
h + 5t^2 = vt....divide both sides by t
(h + 5t^2) / t = v

A triangle has side length of 14 cm 48 cm and 50 cm classify it as acute obtuse or right

Answers

Final answer:

The triangle with side lengths of 14 cm, 48 cm, and 50 cm is a right triangle.

Explanation:

The lengths of the sides of the triangle are 14 cm, 48 cm, and 50 cm. To classify the triangle, we need to determine if it is acute, obtuse, or right.

Using the Pythagorean theorem, we can check if it satisfies the condition for a right triangle. If the square of the length of the longest side (50 cm) is equal to the sum of the squares of the other two sides (14 cm and 48 cm), then it is a right triangle.

In this case, (50)^2 = (14)^2 + (48)^2, which is true. Therefore, the triangle is a right triangle.

Final answer:

A triangle with side lengths of 14 cm, 48 cm, and 50 cm is classified as an acute triangle.

Explanation:

A triangle with side lengths of 14 cm, 48 cm, and 50 cm can be classified as an acute triangle.



To determine this, we need to check if the square of the longest side (50 cm) is less than the sum of the squares of the other two sides (14 cm and 48 cm).



502 < 142 + 482



2500 < 196 + 2304



2500 < 2500



This inequality is not true, so the triangle is not obtuse or right. Thus, it is classified as an acute triangle.

find the nonpermissible replacement for the variable y in this expression (y^2)/(-3y+9) find the nonpermissible replacement for the variable y in this expression (y^2)/(-3y+9)

Answers

The nonpermissible replacement for the variable y in this expression is y = 3.


Substituting y = 3 to the expressions yields:


(3)^2/(-3(3)+9) 


9/0, which is undefined.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

how do you graph this function rule: y = |X| - 7

Answers

x turns positive anywyere you do it

to graph it
graph x=y for all x≥0
now reflect that line across y axis
you get a v
move that whole graph 7 units down

done

If 3x-1=11, then 2x=?

Answers

Final answer:

To find 2x, we first need to solve for x in the equation 3x - 1 = 11. We isolate x by adding 1 to both sides and divide by 3 to obtain x = 4. Finally, multiplying x by 2 gives us 2x = 8.

Explanation:

To solve the equation 3x - 1 = 11 for 2x, we need to isolate x first. Adding 1 to both sides, we get 3x = 12. Dividing both sides by 3, we find that x = 4. Now, to find 2x, we simply multiply x by 2, which gives us 2(4) = 8.

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If x =4 calculate the value of 2x squared - 5

Answers

2x squared - 5 
= 2(x)^2 - 5
= 2(4)^2 - 5
= 2(16) - 5
= 32 - 5
= 27

The sales tax rate in jans town is 7.5.if she buys 3 lamps for $23.59 each and a sofa for $769.99 , how much sales tax does she own ?

Answers

I believe that tax rate are in percent, so tax rate = 7.5%

Now, lets we total the money that she must pay without tax ( just for 3 lamps and 1 sofa ) :
3 lamps = 3 . $23.59 = $70.77
1 sofa = $ 769.99
Total amount = $769.99 + $70.77 = $840.76

We have to find tax amount, the tax amount of the total amount is about 7.5% of the price. Then we have to adding the tax amount into the total amount. So that we have the Total amount including the tax.

tax amount = 7.5% . 840.76 = $63.057
Total amount (inc. tax amount) =
$840.76 + $63.057 = $903.817

Therefore, she must pay those sofa and lamps about $903.817. So expensive huh? =))

Find the missing number in this proportion.

7 / 35 = ? / 28

Answers

Final answer:

To find the missing number in the proportion 7 / 35 = ? / 28, we can use the concept of cross-multiplication. The missing number is 5.6.

Explanation:

To find the missing number in the proportion 7 / 35 = ? / 28, we can use the concept of cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and then setting the two products equal to each other. In this case, we have 7 * 28 = ? * 35. Solving for the missing number, we get:




 7 * 28 = ? * 35
 196 = ? * 35
 ? = 196 / 35
 ? = 5.6



So, the missing number is 5.6.

Abcd is a rectangle. Find the length of each diagonal. .AC= 3y/5 BD=3y-4

Answers

I hope this helps you

Answer:

AC = BD = 1 unit

Step-by-step explanation:

 Given : length of diagonal of rectangle ABCD  [tex]AC=\frac{3y}{5}[/tex] and [tex]BD=3y-4[/tex]

We have to find the length of diagonal.

We know In rectangle diagonal are of equal lengths.

Therefore, for rectangle ABCD diagonals AC= BD

Substitute the values, we get,

[tex]\frac{3y}{5}=3y-4[/tex]

Cross multiply , we get

[tex]3y=5(3y-4)[/tex]

On simplyfy , we get

[tex]3y=15y-20[/tex]

Solve for y , we get

[tex]15y-3y=20[/tex]

[tex]12y=20[/tex]

Divide both side by 12, we get,

[tex]y=\frac{20}{12}=\frac{10}{6}[/tex]

Thus, put the values of y in AC and BD to find the length of diagonals , we get,

[tex]AC=\frac{3y}{5}=\frac{3}{5}\times\frac{10}{6}=1[/tex]

Similarly for BC, we get,

[tex]BD=3y-4=3(\frac{10}{6})-4=5-4=1[/tex]

Thus, AC = BD = 1 unit

The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card
(State wether the graph of the linear relationship is a solid line or a set of unconnected points.

Answers

if the cost of the school lunch does not change it would be a linear equation, therefor, you would connect the dots.

isabella bought 1.1 kilograms of top quality hamburger meat at $5.00 per kilogram. how much did it cost?

Answers

1.1 kg * $5 / kg = $5.50

The cost of 1.1 kilograms of hamburger meat at $5.00 per kilogram is $5.50

Multiply the weight of the meat (1.1 kg) by the price per kilogram ($5.00):

1.1 kg x $5.00/kg = $5.50.

Therefore, it cost Isabella $5.50 to buy 1.1 kilograms of top-quality hamburger meat.

Find the area of the region. Use a graphing utility to verify your result.
y = 6 sin(x) + sin(6x)

the graph goes from x=0 to x=pi ...?

Answers

[tex] \int\limits^\pi_0 [6 \sin{x} + \sin(6x) }] \, dx \\ \int\limits^\pi_0 {6 \sin{x}}\ dx + \int\limits^\pi_0 \sin(6x) } \ dx \\ 6\int\limits^\pi_0 { \sin{x}}\ dx + \frac{1}{6} \int\limits^{6\pi}_0 \sin{t} } \ dt \\ -6\cos{x}|_0^\pi- \frac{1}{6}\cos{t}|_0^{6\pi} \\-6(\cos\pi-\cos0)-\frac{1}{6}(\cos{6\pi}-\cos0) \\ -6(-1-1)-\frac{1}{6}(1-1) \\-6(-2)-\frac{1}{6}\times0 \\12[/tex]
Final answer:

To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval. Using a graphing utility, we can plot the function and verify the result.

Explanation:

To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval.

Using a graphing utility, we can plot the function and verify the result. The integral will give us the area under the curve.

A graphing utility like Desmos or Wolfram Alpha can be used to plot the function and find the area under the curve.

Which of the following is the best estimate for the capacity of a bottle of salad dressing?

1 fl oz
1 gal
1 pt
I'm just having trouble picturing a bottle of salad dressing... I don't use it that often. ...?

Answers

The best and most correct answer among the choices provided by your question is the first choice.

1 fl oz is the best estimate for the capacity of a bottle of salad dressing.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Answer:

1 gal

Step-by-step explanation:

What does the inequality x + 3 ≤ 2 say?

A number and three is at most two.
A number and three is less than two.
A number and three is at least two.
A number and three is no less than two.

Answers

A number and three is at most 3.

Answer:

A number and three is at most 3.

Step-by-step explanation:

Factor completely: 2x2 + 6x − 80

(2x − 5)(x + 8)

(2x − 10)(x + 8)

2(x − 5)(x + 8)

2(x − 10)(x + 8)

...?

Answers

Correct answer is C.

[tex]2x^2+6x-80 \\2(x^2+3x-40) \\2(x^2+8x-5x-40) \\2(x(x+8)-5(x+8)) \\2(x+8)(x-5)[/tex]

Quadratic functions are functions that has a degree of 2. The factored form of the function is (2x-10)(x+8)

Factorization of functions

Quadratic functions are functions that has a degree of 2. Given the function below;

2x^2 + 6x - 80

Factorize

2x^2+16x - 10x - 80

Group

(2x^2+16x)-(10x+80)

Factor out the GCF

2x(x + 8)-10(x+8)

(2x-10)(x+8)

Hence the factored form of the function is (2x-10)(x+8)

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find two consecutive odd integers whose sum is -88

Answers

Instead of guessing (guess and check)  or me giving you the answer, lets solve this mathematically.

first number is x. Second number is the next (or consecutive) odd number so its x+2 (can also do x-2)

Using (x+2)
x + (x+2) = -88
2x = -90
x = -45
and the other number will be -43

Using (x=2)
x + (x-2) = -88
2x = -86
x = -43
and the other number will be -45


The answer: -45, -43.
______________________
Explanation:
_________________________________
Let "x" = one of the odd integers.

Let "x + 2" = the other odd integer.
_________________________________
x + (x + 2) = - 88 ;

x + x + 2 = - 88;

2x + 2 = - 88 ;  Now, subtract "2" from EACH side of the equation:
_______________________
2x + 2 - 2 = - 88 - 2 ; to get:
______________________________
2x = -90 ; Now, divide EACH side of the equation by "2"; to isolate "x" on one side of the question; and solve for "x"; 
_________________________________
2x/2 = -90/2 ;
______________
x = -45
_________
So one of the integers is -45.  It is an odd number? Yes!

The next consecutive integer is: "(x+2)" ; or, (-45 + 2) = -43. Its it an odd number? Yes!

Are "-45", and "-43" consecutive odd integers? Yes!
_______________________________
The two consecutive integers are: -45 and -43.
_________________________
To check our work:
___________________
Do the sum of our two consecutive integers equal -88?
___________
-45 + (-43) =? -88 ?  Yes!
___________________________

can someone please explain?

Show that the point (7/25, 24/25) is on the unit circle

Answers

The unit circle has all points which has a distance of 1 from the origin. We check the distance of this point using:

d = √(x² + y²)
d = √[(7/25)² + (24/25²)]
d = 1

So this point does lie on the unit circle.
Final answer:

To show that the point (7/25, 24/25) is on the unit circle, we need to demonstrate that its distance from the origin is equal to 1.

Explanation:

To show that the point (7/25, 24/25) is on the unit circle, we need to demonstrate that its distance from the origin is equal to 1.

The distance between two points, (x1, y1) and (x2, y2), is given by the formula: √((x2-x1)² + (y2-y1)²).

In this case, the distance between the point (7/25, 24/25) and the origin (0, 0) can be calculated as: √((7/25-0)² + (24/25-0)²) = √((49/625) + (576/625)) = √(625/625) = 1.

Since the distance between the given point and the origin is indeed equal to 1, we can conclude that the point is on the unit circle.

Solve the system by substitution.
2x - y + z = -4
z = 5
-2x + 3y - z = -10

Answers

Substituting z = 5 into the first equation:

2x - y + 5 = -4
y = 2x + 9

Substituting y and z into the third equation
-2x + 3(2x + 9) - 5 = -10
4x + 27 = -5

x = -8
y = 2(-8) + 9 = 7
z = 5

Answer: a

Step-by-step explanation: that person coulda said that

A painting measures 15 cm long by 24 cm high. You buy two posters, each showing an enlargement of the painting. The first poster measures 45 cm long by 72 cm high. The second poster measures 97.5 cm long by 156 cm high. Which of the following is true? (Hint: To be an accuarate representation of the painting, would the the poster be similar to the painting?)

Answers

The Answer to your question is A. Both posters are accurate representations of the painting. 

I had the same thing. Please mark as Brainiest Answer.

Answer:

Both posters ARE accurate representations of the painting

Step-by-step explanation:

Gradpoint

NEED YOUR HELP!! I WILL UPVOTE!
Combining Like Terms:

Solve the equations by combining like terms. Show all the steps.
Then write two of your own problems where you combine like terms. Show all steps, as well as your solution.
1. 16x − 4x = -48

Answers

12x=-48 (divide 12 from both sides)
x=-4

10y-13y=30
-3y=30 (divide -3 from both sides)
-10=y

10x+14x=48
24x=48 (divide 24 from both sides)
x=2


Angle ABD and angle BDE are supplementary. Find the measures of both angles.

m angle ABD =5x degrees, m angle BDE = (17x-18)degrees

Answers

By definition of supplementary angles,
∠ABD + ∠BDE = 180
5x + 17x - 18 = 180
22x = 198
x = 9

∠ABD = 5(9) = 45°
∠BDE = 180 - 45 = 135°

An open box with a volume of 1500 cm cube is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of side length x cm from each corner, and folding up the sides. Find the exact dimensions of the box.

Answers

The dimensions of the box formed will be:
width: 20 - 2x 
length: 40 - 2x
height: x

Volume = width x length x height
1500 = x(20 - 2x)(40 - 2x)
1500 = x(800 + 4x² - 120x)
1500 = 4x³ - 120x² + 800x
0 = 4x³ - 120x² + 800x - 1500
0 = x³ - 30x² + 200x - 375
Solving the cubic equation:
x = 5 (only integer root)

Length = 30 cm
Width = 10 cm
Height = 5 cm

If your teacher tells you to do questions 28 through 41 in your math book for homework, how many questions is that?

(Do not include units in your answer.)



Answers

41-28=13 questions, but you also have to do 41 and 28, so 15 questions

Answer:

14 questions.

Step-by-step explanation:

We have been given that your teacher tells you to do questions 28 through 41 in your math book for homework. We are asked to find he total number of questions.

Since we need to solve questions 28 through 41, this means we have to solve question number 28 and 41 as well.

We know that 28-37 would be 10 questions and 38-41 would be 4 questions.

[tex]\text{Total questions}=10+4[/tex]

[tex]\text{Total questions}=14[/tex]

Therefore, you need to solve 14 questions to complete the homework.

Which function has the greatest y-intercept? (2 points)


f(x)

g(x)

h(x)

All three functions have the same y-intercept.

Answers

Final answer:

The function h(x) has the greatest y-intercept of 8, as it crosses the y-axis at the highest point.

Explanation:

The function that has the greatest y-intercept is the one that crosses the y-axis at the highest value. The y-intercept is the point where the graph of a function intersects the y-axis, which is when x = 0. So, to find the function with the greatest y-intercept, we need to evaluate the y-value when x = 0 for each function.

Let's consider the functions f(x), g(x), and h(x). If f(x) has an equation of y = 3x + 5, g(x) has an equation of y = x - 2, and h(x) has an equation of y = -2x + 8, we can plug in x = 0 and see which function gives us the greatest y-value.

For f(x), when x = 0, y = 3(0) + 5 = 5. For g(x), when x = 0, y = 0 - 2 = -2. And for h(x), when x = 0, y = -2(0) + 8 = 8. Thus, h(x) has the greatest y-intercept because it crosses the y-axis at the highest point, which is 8.

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A sweater that originally cost $40 is on sale for 10 percent off. What is the amount of the discount?
$2
$4
$30
$36

Answers

x percent = x/100
10 percent = 10/100 = 0.10

10% of $40 = 0.10*40 = 4

You save $4

The old price is $40 and changes to $36 after the discount is applied. This is ignoring any taxes or other surcharges

Anyways I'm going a bit off tangent. The final answer is choice B) $4

Answer:

B) $4

Step-by-step explanation:

What is the general term for the sequence 1,6,11,16,...?

n + 5
5n - 4
5n + 1

Answers

5n-4
Just plug numbers into it. Make this a table.
n 0 1 2 3 
y 1 6 11 16

Answer:

Step-by-step explanation:

The given sequence is:

1,6,11,16,...

Since, the sequence is Arithmetic progression, therefore

The general term for the sequence is:

[tex]A_{n}=a+(n-1)d[/tex]

where a is the first term of the sequence and d is common difference.

Substituting the given values, we get

[tex]A_{n}=1+(n-1)5[/tex]

[tex]A_{n}=1+5n-5[/tex]

[tex]A_{n}=5n-4[/tex]

which is the required general term.

Thus, option B is correct.

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