Given the function g(x)=41x^3+a for some constant a, which describes the inverse function g^-1(x)

Answers

Answer 1

Answer:

[tex]g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}[/tex]

Step-by-step explanation:

The inverse of a function has [tex]x[/tex] and [tex]y[/tex] values switched from the original function. Therefore, simply switch [tex]x[/tex] and [tex]y[/tex] and isolate [tex]y[/tex] to get your inverse function:

Original function: [tex]g(x)=41x^3+a[/tex]

Switching [tex]x[/tex] and [tex]y[/tex], then isolating [tex]y[/tex]:

[tex]x=41y^3+a,\\x-a=41y^3,\\\frac{x-a}{41}=y^3,\\y=\sqrt[3]{\frac{x-a}{41}}[/tex].

Therefore, the inverse of the [tex]g(x)=41x^3+a[/tex] is:

[tex]\fbox{$g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}$}[/tex].


Related Questions

The formula for the velocity of an object is v=d/t, where v is the velocity of an object, dis the distance traveled, and t is the time elapsed, while the distance is traveled. If you had only this formula to work with, what should your first step be in determining how long it takes for light to reach Earth from the Sun? What additional information do you need to calculate this?

Answers

Answer:

To know the distance between the sun and the earth you need isolate d of the equation:

[tex]v = \frac{d}{t} \\ d = vt[/tex]

and the additional information needed is the velocity of light and the time elapsed to be in the earth

Can someone help me with this please

Answers

Answer:

the picture is upside down

Step-by-step explanation:

I can’t see right please do it again

What is -20 + 1/2 in a decimal form

Answers

Answer: The answer is -19.5

Step-by-step explanation: This is because 1/2 is .5 in decimal form. A negative PLUS a positive = is negative since the -20 is larger than .5

Answer:

the answer would be -19.5 :)

Step-by-step explanation:

Help! I’m trying to help my friend get caught up who had been ill.

Answers

Answer:

down below

Step-by-step explanation:

i answered so that the other guy can get a brainliest:)

Please help! Or if someone can explain how to find the answer

Answers

Answer:

If the equation is in the form, ax + b = c, where x is the variable, you can solve the equation as before. First “undo” the addition and subtraction, and then “undo” the multiplication and division. Solve 3y + 2 = 11. Subtract 2 from both sides of the equation to get the term with the variable by itself.

Answer: x = 20

All this is exaple hople it help

the answer to this is20, hope it helps <3

WORTH 65 PTS PLEASE ANWSER AS SOON AS POSIBLE The ratio between the number of girls and the number of boys in a school is 3 : 4 if the number of boys is 140, find the number of girls

Answers

Answer:

105 girls

Step-by-step explanation:

The ratio between girls and boys is 3:4, which means for every  3 girls, there are 4 boys. We are trying to solve for the number of girls, so the ratio will be x:140. First let's divide 140 by 4 to find out the value of each part.

We will get 35 for each part.

Multiply 35 by 3 to get 105. There we find that there are 105 girls for 140 boys. Hope this helped :)

8 divided by the sum of 9 and 3?
6 divided by the sum of 7 and 6?

Answers

Answer:

1. 0.66666666666

2. 0.46153846153

Step-by-step explanation:

8 divided by the sum of 9 and 3 is basically just 8 / ( 9 + 3 )

6 divided by the sum of 7 and 6 is basically just 6 / ( 7 + 6 )

Dj Jacqueline is making a playlist for a friend: she is trying to decide what 15 songs to play and in what order they should be played. If she has her choices narrowed down to 10 pop. 25 reggae, and 10 blues songs, and she wants to play an equal number of pop. reggae, and blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place

Answers

Answer:

4.4 * 10^21

Step-by-step explanation:

Given :

Number of pop, n(p) = 10

Number of reggae, n(r) = 25

Number of blues, n(b) = 10

Total number of songs to select (n) = 15

If she wants equal Number if the 3 genres

Each genre will have : 15/3 = 5 songs each

Hence,

(10C5 * 25C5 * 10C5) * n!

Combination formula :

pCr = p! / (p-r)! r!

Using calculator to save computation time :

(10C5 * 25C5 * 10C5) * n!

(252 * 53130 * 252) * 15!

= 4412050844368527360000

= 4.4 * 10^21

Why is a sample used more often more than a population

Answers

Answer:

A number which describes a characteristic of a population. ... Uses a sample to find conclusions, analyzations, and probability about a population. Why is a sample used more often than a population? Because it is more difficult to get an accurate population where as a sample is smaller and easier to assess.

Which which equation is standard form has a graph that passes through the point -4 2 and has a slope of 9/2

Answers

Answer:

Equation of straight line that passes through (-4, 2) and has slope 9/2 is

[tex]y-2=\frac{9}{2} (x+4)[/tex]

Step-by-step explanation:

Equation of straight line in point slope form is given as

[tex]y-y_1=m(x-x_1)[/tex] ---------(2)

Here

[tex]m = \frac {9}{2}[/tex]   and  [tex](x_1, y_1) = (-4, 2)[/tex]

Substituting values in equation (1)

[tex]y-2=\frac{9}{2} (x+4)[/tex]

pls help me, i’ll give brainly

Answers

Answer/Step-by-step explanation:

First, find the slope (m) of Line L using the points (0, 5) and (2, 1):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 5}{2 - 0} = \frac{-4}{2} = -2 [/tex]

Slope (m) = -2

✔️Since the line is parallel bro Line L, it would also have the same slope value of -2.

We can use the slope (m) and a point (a, b) of the line to find its equation using the point-slope formula, y - b = m(x - a).

Substitute (a, b) = (3, 0), and m = -2 into y - b = m(x + a):

Thus,

✅y - 0 = -2(x + 3)

Rewrite equation in slope-intercept form

y = -2(x + 3)

✅y = -2x - 6

whats the unit rate of 4 and 3/4

Answers

Answer:

3/16

Step-by-step explanation:

Please help me and I'll give you Brainly star

Answers

Answer:
X = 30 degrees

Explanation:
Angle BAC = 60 degrees because of equilateral triangle. Therefore angle BAD = 120 degrees because of angles on a straight line

Angle CBA = 60 degrees, therefore angle DBA = 30 degrees because line DB and BC meet at 90 degrees.

Now do 180 - (30 + 120) = 30. X = 30

If BD bisects ∠ABC, find each value

Answers

Answer:

x=14

y=10

AD=19

CD=19

Step-by-step explanation:

x:

5x-6=64

   +6   +6

5x=70

x=14

y:

3y-11=y+9

   +11    +11

3y=y+20

-y   -y

2y=20

y=10

AD:

3y-11

3(10)-11

30-11

19

CD:

y+9

(10)+9

19

hhhhhhheeeeeeeeeeellllllllllllllllpppppppppp mmmmmmmmmeeeeeeeeeeee pppppppplllllllllleeeeeaaaaaaaaassssseeeeee!!!!!!!

Answers

35 Celsius but it really depends on your opinion

If x=-3 what does 6+5x

Answers

Answer:

-9

Step-by-step explanation:

Plug in -3 for the x value to get 6 + 5 (-3).  Multiply 5 by -3 to get -15 and subtract that number from 6 to get -9 as your final answer.

When Josh babysits, he charges a flat fee of $14 plus an
hourly rate of $9. How long would Josh need to babysit if he
wants to earn $86 in one night?

Answers

Answer:

8

Step-by-step explanation

86-14=72 this is the hourly rate before the flat fee is added on. Now you have to divide $72 by $9 to see how many hours josh needs to work. Josh gets paid $9 an hour so he needs to work for 8 hours in order to get $72. Then add the flat fee of 14 and you get $86

Area of composite shape
Find the area of the shape shown below.
1
12
13
6

Answers

sorry but where is the photo?

write the slope of x+2y=16 pls help fast

Answers

Answer: [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

To find the slope, let's turn the equation into slope-interept form. In slope intercept form, y=mx+b, we know that m=slope.

[tex]x+2y=16[/tex]             [subtract both sides by x]

[tex]2y=-x+16[/tex]          [divide both sides by 2]

[tex]y=-\frac{1}{2}x+8[/tex]

Now, we know that [tex]m=-\frac{1}{2}[/tex]. That tells us [tex]-\frac{1}{2}[/tex] is the slope.

Step-by-step explanation:

x+2y=16

-× -×

2y=-x+16

÷2. ÷2

y=-1/2x+8

slope is -1/2

help please....and thank you

Answers

yards i’m pretty sure.

Image P is shown in the coordinate grid Image P is translated 2.5 units to the right and 3.5 units up to create image P'.
6
Image P
1
2 3
4
Which rule describes this transformation?

Answers

Answer:

Here we do not have the image P, but let's solve this in a general way.

Suppose that we have a point A (x,y)

If we translate the point A n units horizontally (where n can be positive, translation to the right, or negative translation to the left.)

The new point will be (x + n, y)

if we translate the point m units vertically (if m is positive the translation is upwards, if m is negative the translation is downwards), the new point will be (x + n, y + m)

Then if our figure was p (x, y)

The new figure is p(x + 2.5, y + 3.5)

So for every point in the figure, we need to add 2.5 to the x component, and 3.5 to the y-component.

Solve for x.
ASAP, please help me

Answers

Answer:

8

Step-by-step explanation:

180=90+40+6x+2

180=132+6x

48=6x

x=8

Answer:

x=4 i think havent done this in a long time

Step-by-step explanation:

Two angles are complementary if their sum is 90o. If one angles measure is xo and the other angle is (2x – 3)o find the measure of each angle.

Answers

x + (2x - 3) = 90
3x - 3 = 90
3x = 93
x = 31
angle 1 = 31
angle 2 = 59

PLEASE HELP AND ANSWER ALL 3

Answers

Answer: 10.) -6 and it's B

11.) A

12.) C

Step-by-step explanation:

please help me i cant under stand this

Answers

Answer:

Plot the same points that are on the table

Step-by-step explanation:

when given a table you are also given ordered pairs , so for example , the first pair on the table is (1,3) so plot that as your first point , then your second is (2,6) and so on . write these on the blank spaces aswell ! hope this helps :))))

One-third x + one-sixth y = 2. When x is 3, 1 x + StartFraction 3 Over 6 EndFraction y = 6. One-half x + three-fourths y = negative 3. When x is negative 2, negative 1 x minus StartFraction 6 Over 4 EndFraction = 6. Negative 1 y = 12.
Continue solving the system of equations.

What is the solution to the system?

(
,
)

Answers

Answer:

(12, -12)

Step-by-Step:

I got it right on Edge 2021

Answer:

its 12,-

12

Step-by-step explanation:

Mr. Marcus is splitting a huge new pack of colored pencils equally among 25 students after splitting the pencils he has 4 left if there were 429 colored pencils to begin with how many did each student receive

Answers

Answer:

hIm so sorry for that other person they did the same thing to my answer and a bunch of other people too iecked there account and reported him many times so sorry but can give you the answer :)

Its 17 if i id math correctly! sorry bout the other person have a great day

Step-by-step explanation:

Answer is no longer needed..

Answers

Answer:

WARNING DO NOT JOIN THE ZOOM OF 825 338 1513⚠ OR DO NOT JOIN ANY ZOOMS FROM ANYONE EXCEPT REAL LIFE FRIENDS OR FRIENDS FAMILY OR TEACHERS! HIS ZOOM NAME IS Mysterious Men HE ASKS GIRLS TO DO INAPPROPRIATE THINGS PLS COPY AND PASTE THIS TO OTHER COMMENT SECTIONS! PLS PASS THIS AROUND!

Mr. Garza had 178 pencils in a storage room. He put 46 more boxes of pencils in the storage room. Each box contained 12 pencils. Which of these is the best estimate of the number of pencils Mr. Garza now has in his storage room?

Answers

Answer: 730

Step-by-step explanation:

46x12+178= 730

Can you guys help me quickly

Answers

the first one is 20
the second one is 10
hope this helped
First on = 20
Second one = 10
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