f (x) = 6x + 4. Find the inverse of f(x).
O A. f-1 (2) = 4 - 6x
O B. f-1(x) = 6x - 4
O c. f-(x) =
O D. f-'(x) = 20
2-4
-6
Answers
If [tex]f^{-1}(x)[/tex] is the inverse of f(x), then
[tex]f\left(f^{-1}(x)\right) = x[/tex]
By definition of f(x), we have
[tex]f\left(f^{-1}(x)right) = 6f^{-1}(x) + 4 = x[/tex]
Solve for the inverse :
[tex]6f^{-1}(x) + 4 = x[/tex]
[tex]6f^{-1}(x) = x - 4[/tex]
[tex]f^{-1}(x) = \dfrac{x-4}6[/tex]
which makes C the correct choice.
Related Questions
A paper company ships notepads in rectangular boxes that have dimensions measuring 9 inches long, 9 inches wide, and 10 inches tall. Show work. Complete sentences.
V = LWH The volume of a rectangular prism / cube is equal to the length times the width times the height.
a. What is the volume of the box?
b. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the volume of each notepad?
c. What is the maximum number of notepads that will fit in 1 closed box
i will give brainliest :)
Answers
Answer:
a. 810
b. 27
c. 30
Step-by-step explanation:
Part a.
The volume is 9 * 9 * 10.
9 * 9 = 81, and 81 * 10 = 810.
Part b.
The volume of a cube is x^3, where x is the side length of the cube.
If x = 3, then 3^3 = 27.
Part c.
If each notebook has a volume of 27, then the maximum amount of notebooks that will fit in a box with volume 810 is 810/27 = 30 notebooks
a. The volume of the rectangular box is 810 inch³.
b. The volume of the notepad is 243 inch³.
c. The maximum number of notepads that will fit inside the box is 3.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, A paper company ships notepads in rectangular boxes that have dimensions measuring 9 inches long, 9 inches wide, and 10 inches tall.
Therefore, The volume of the box is, = (9×9×10) inch³.
= 810 inch³.
The dimensions of the notepad are 9 inches by 9 inches with an height of 3 inches.
Therefore, The volume of the notepad is = (9×9×3) = 243³ inches.
The maximum number of notepads that will fit inside thebox is,
= (810/243).
= 3.33 but it sholud only be 3 notepads.
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Hurry!! Answer it please:))
Answers
Answer:
Option C.
Domain:
{3, 0, 2, 4}
Step-by-step explanation:
The domain is the set of all the values of x.
Answer:
C is the answer!:)
Step-by-step explanation:
Domain is all numbers on the left and range is on the right
what is the value of x in m(x+n)=n
Answers
The equation m(x + n) = n si solved for x will be given as x = n / m (1 - m).
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation is given below.
m(x + n) = n
By simplifying for x, then we have
x + n = n / m
x = n / m - n
x = (n - mn) / m
x = n / m (1 - m)
More about the linear system link is given below.
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What’s the answer to the equation
Answers
Answer:
To solve an equation is to determine the values of the variable that make the equation a true statement. Any number that makes the equation true is called a solution of the equation. It is the answer to the puzzle!
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8593 g and a standard deviation of 0.0511 g. A sample of these candies came from a package containing 464 candies, and the package label stated that the net weight is 396.1 g. (If every package has 464 candies, the mean weight of the candies must exceed 396.1 464=0.8537 g for the net contents to weigh at least 396.1 g.)
Answers
Answer:
The package label stated that the net weight is 381.8g If every package has ... brand of candies have a mean weight of 0.8616g and a standard deviation of ...
The function f is given by f(x)=(x^{3}+bx+6)(g(x)), where b is a constant and g is a differentiable function satisfying g(2)=3 and g′(2)=−1. For what value of b is f′(2)=0?
7
10
12
22
Answers
Answer:
[tex]\displaystyle b = -22[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = (x^3+bx+6)(g(x))[/tex]
Where b is a constant and g is a differentiable function.
And we want to determine the value of b such that f'(2) = 0.
Find f' using the product rule:
[tex]\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ (x^3+bx+6)(g(x))\right] \\ \\ & = \frac{d}{dx}\left[ x^3 + bx + 6\right] g(x) + (x^3+bx+6)\frac{d}{dx}\left[ g(x)\right] \\ \\ & = (3x^2+b)(g(x)) + (x^3 + bx + 6)(g'(x))\end{aligned}[/tex]
Substitute using known values and solve for b:
[tex]\displaystyle \begin{aligned}f'(2) = 0 & = (3(2)^2+b)(g(2)) + ((2)^3+b(2)+6)(g'(2)) \\ \\ 0 & = (12+b)(3) + (14+2b)(-1) \\ \\ 0 & = 22 +b \\ \\ b & = -22\end{aligned}[/tex]
In conclusion, the value of b is -22.
The function f is given b is a constant and g is a differentiable function the value b (-8.4),
Let's start by finding the derivative of the given function f(x) with respect to x:
f(x) = (x³ + bx + 6) × g(x)
Using the product rule for differentiation, the derivative of f(x) is:
f'(x) = (x³ + bx + 6) × g'(x) + g(x) × (3x² + b)
Now we are interested in finding the value of b for which f'(2) = 0. So, let's plug in x = 2 and use the information given about g(2) and g'(2):
f'(2) = (2³ + 2b + 6) × g'(2) + g(2) × (3 × 2² + b)
Since g(2) = 3 and g'(2) = -1,
f'(2) = (8 + 2b + 6) × (-1) + 3 × (3 × 4 + b)
= (2b + 14 - 8) + 3× (12 + b)
= 2b + 6 + 36 + 3b
= 5b + 42
Now, we want to find the value of b for which f'(2) = 0:
5b + 42 = 0
Subtracting 42 from both sides:
5b = -42
Dividing both sides by 5:
b = -8.4
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Complete question:
The function f is given by f(x)=(x^{3}+bx+6)(g(x)), where b is a constant and g is a differentiable function satisfying g(2)=3 and g′(2)=−1. For what value of b is f′(2)=0?
7
10
12
22
-8.4
Let f(x)=5(3)x−4. Evaluate f(6).
Answers
5(3)(6)-4
15(6)-4
90-4
86
hope it helps
Given that:
f(x) = 5(3)x-4
f(6) = 5(3)(6) - 4 ⇛15(6) - 4 ⇛90-4 ⇛86Ans.
1. Kim's age is three times that of her sister. When you add Kim's age to her sister's age, you get 48. How old is each sister? (a) Write an equation that represents the situation. Explain any variable used. (1 point) (b) Solve the equation from Part (a). Show your work. (4 points)
Answers
Answer:
3k=48
Step-by-step explanation:
k=kim's age
3k=48
/3
k=16
A pianist charges $200 to perform at a restaurant. At the end of the night she collected her tips and left with a total earning of $310. Write an equation and solve for the amount she made in tips for the performance.
Answers
Answer:
310-200= T
Step-by-step explanation:
310 = 200 + x
Let’s break this down. 310 is their total earning, 200 is our set price for performing, and x represents how much she earned in tips.
310 = 200 + x
110 = x
Hope this helps!
someone help me with my assignments
Answers
Answer: Choice A
Step-by-step explanation: You are given the inequality g is less than or equal to. Greater/less than and equal to, you use solid circle. Greater/less than, you use open circle. From there, you just look at the inequality in which direction is it going at and from there, you should be able to select your choice which happens to be the first one.
I hope this explanation helps.
Best to you!
most of the mathematical symbols were not invented until 16th century, before that how equations were written?
Answers
Answer:
During the 16th and early 17th Century, the equals, multiplication, division, radical (root), decimal and inequality symbols were gradually introduced and standardized. ... In the Renaissance Italy of the early 16th Century, Bologna University in particular was famed for its intense public mathematics
Prior to the invention of the Mathematical Symbols, mathematical equations were written in words.
For example, Y + 10 = 4.5 would be written as
The thing plus ten equal to eight.
It is true that MOST, that is, the majority of the mathematical symbols we have today were invented in the 16th century. Examples of such symbols are:
Multiplication Sign × (1618)Plus/Minus Sign ± (1628)Inequality Signs > and < (1631)Percentage Sign % (1650)Infinity Sign ∞ (1655)Division Sign ÷ (1659) to mention a few.Prior to the 16th century, some mathematical signs were already in use. They are:
Plus Sign + (1360)Minus Sign - (1489)Square Root Sign (1525)Equals Sign = (1557) to mention a few.See the link below for more about Mathematical Signs:
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i need help btw im 6th grader
Answers
- 5.3
———-
17.97
:)
A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be % confident that his estimate is in error by no more than percentage point Complete parts (a) through (c) below.
A) Assume nothing is known about the percentage of computers with new operating systems
n =
round up to the nearest integer
b) Assume that the recent survey suggest that about 96% of computers use a operating system.
n =
round up to the nearest integer
C) Does the additional survey information from part (b) have much of an effect on the sample size that is required?
A.
Yes, using the additional survey information from part (b) dramatically reduces the sample size.
B.
No, using the additional survey information from part (b) does not change the sample size.
C.
Yes, using the additional survey information from part (b) dramatically increases the sample size.
D.
No, using the additional survey information from part (b) only slightly increases the sample size.
Answers
Using the z-distribution, we have that:
a) A sample of 601 is needed.
b) A sample of 93 is needed.
c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
For this problem, we consider that we want it to be within 4%.
Item a:
The sample size is n for which M = 0.04.There is no estimate, hence [tex]\pi = 0.5[/tex][tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2[/tex]
[tex]n = 600.25[/tex]
Rounding up:
A sample of 601 is needed.
Item b:
The estimate is [tex]\pi = 0.96[/tex], hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2[/tex]
[tex]n = 92.2[/tex]
Rounding up:
A sample of 93 is needed.
Item c:
The closer the estimate is to [tex]\pi = 0.5[/tex], the larger the sample size needed, hence, the correct option is A.
For more on the z-distribution, you can check brainly.com/question/25404151
Jessica made $156 for 12 hours of work.
At the same rate, how much would she make for hours of work?
Answers
Answer:
156/12=13
so makes 13 dollars a hour
Hope This Helps!!!
A polygon with both equal angles and equal sides is called
Answers
Answer:
It's called a regular polygon
Answer:
A regular Polygon
Step-by-step explanation:
The width of a rectangle is 6x−6.5 feet and the length is 6.5x+7 feet. Find the perimeter of the rectangle.
Answers
Answer: 25x+1
Step-by-step explanation:
We cam make an equation to find the perimeter, [tex]2(6x-6.5)+2(6.5x+7)[/tex].
then we can simplify it to [tex]12x-13+13x+14[/tex], which we can then further simplify to 25x+1
A force of 18 lb is required to hold a spring stretched 2 in. beyond its natural length. How much work W W is done in stretching it from its natural length to 7 in. beyond its natural length
Answers
Answer:
Step-by-step explanation:
Average force is (19 + 0)/2 = 9 lb
2 inches = 1/6 ft
W = Fd = 9(1/6) = 1.5 ft•lb
help please please help
Answers
Answer:
24/35
Step-by-step explanation:
Hope this helps!:)
Which expression has a coefficient of 4?
A
(2^x)+4
B
4(2^x)+1
C
2(x^4)+1
D
2(4^x)+1
Answers
Answer:
Option D
Step-by-step explanation:
[tex]\\ \sf\longmapsto 2(4^x)[/tex]
You have to first find 4^x and then multiply it with two .Not like this
[tex]\\ \sf\longmapsto 2(4^x)=8^x [/tex](×)
Hence the variable has coefficient 4 as 4^x is multiplied.
Ms. Chapman wants to take her scout troop to Neon Nights roller rink. The employee she spoke to ahead of time said the total cost for all 9 people in the group would be $81. This includes an entrance ticket and a $3 skate rental fee for each person. Which equation can you use to find t, the cost of each entrance ticket? How much does each entrance ticket cost? $
Answers
The cost of the entrance ticket is $6.
The equation that can be used to represent the information in the question is:
Total cost = (number of students x entrance fee) + (cost to rent a skate x number of students)
$81 = 9t + ($3 x 9)
$81 =9t + $27
In order to determine the value of t, the following steps would be taken:
Combine similar terms
$81 - $27 = 9t
Subtract similar terms
54 = 9t
Divide both sides of the equation by 9
t = $6
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Pencils can be purchased in packages of 12 or 25. If Karl purchased 8 packages to get 135 pencils, how many packages of 12 did he buy?
Answers
Answer: 60
Step-by-step explanation:
list all of the multiples and choose the least common number
10: 10 20 30 40 50 60 70 80 90 100
12: 12 24 36 48 60 72 84 96
find a number that shares all the prime factors of the two numbers
prime factors of 10: 2, 5
prime factors or 12: 2, 2, 3
LCM = 60
how can you find 72-25? circle all the correct answers
Answers
Answer:
eeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
Simplify.
57.8 – 4.07
Answers
Answer:
53.73
Step-by-step explanation:
PLEASE HELP!!!
True or false
3(x-2) and 3x-6 are
equivalent
Answers
Answer:
true!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
True.
Step-by-step explanation:
They are equivalent expression because if you distribute the 3 in 3(x-2), you will get the same expression as 3x-6.
3(x-2) =
(3*x) - (3*2) =
3x - 6
Hope this helps.
What is the sum of £4(0.5) "1?
n=1
O S=1.5
OS = 2
O S = 4.5
O S= 8
Answers
I need help with this please
Answers
Answer:
I’m not sure what that means but I think it’s the one with the blue
Step-by-step explanation:
Can somebody help me as soon as possible I’ll give brainliest
Answers
Find the Value for X,Y and z using Gauss-Jordan Inversion method
2X+3Y=4
X+2Y=2
Answers
Answer:
x = 2 y = 0
Step-by-step explanation:
Answer:
Step-by-step explanation:
Multiply.
[−3⋅914]⋅[(−0.1)⋅(−28)]
What is the product?
Answers
Answer:
x=5.3984
Step-by-step explanation:
help how do I do this!!!!
Answers
Answer:
C
Step-by-step explanation:
Since the weight is proportional to the cost, let's find the slope of the chart.
(x,y) corresponds to (weight, cost)
Pick 2 coordinate points with both the weight and cost.
(4, 23.96) (6, 35.94)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{35.94-23.96}{6-4}= 5.99[/tex]
One pound is 5.99 dollars.
So to fill in the chart, multiply 5.99 by the number of pounds.
y=5.99x
2 lbs | $11.98
3 lbs | $17.97
4 lbs | $23.96
5 lbs | $29.95
6 lbs | $35.94
With this information, C would be the correct answer.