Answer:
The inverse of [tex]\displaystyle{f(x)=4x^3+8}[/tex] is determined to be [tex]{f^{-1}(x)=\sqrt[3]{\frac{1}{4}x-8}[/tex].
Step-by-step explanation:
In order to find the inverse of a function, we need to know a couple of rules about functions.
f(x) = yTo find the inverse, we flip the y-variable with the x-variables and solve for y.Following these rules, our function now becomes [tex]\displaystyle{x=4y^3+8}[/tex].
We now can simplify it further in order to find the value of x.
[tex]\displaystyle{x=4y^3+8}\\\\4y^3=x-8\\\\y^3=\frac{x}{4}-8\\\\\sqrt[3]{y^3}=\sqrt[3]{\frac{x}{4}-8} \\\\y = \sqrt[3]{\frac{1}{4}x-8}\\\\f^{-1}(x)= \sqrt[3]{\frac{1}{4}x-8}[/tex]
Therefore, the inverse of [tex]\displaystyle{f(x)=4x^3+8}[/tex] is [tex]\displaystyle{f^{-1}(x)=\sqrt[3]{\frac{1}{4}x-8}[/tex].
Answer:
[tex]\huge\boxed{f^{-1}(x) = \sqrt[3]{\frac{x-8}{4}}}[/tex]
Step-by-step explanation:
In order to find the inverse of a function, we need to follow a series of steps.
1. Write the function in the form [tex]y=ax^b+c[/tex]
2. Swap where the x and y values are
3. Solve for y
4. Convert into [tex]f^{-1}(x)[/tex] form
So first, we can write [tex]f(x)=4x^3+8[/tex] as [tex]y=4x^3+8[/tex].
Now we need to swap where the x and y variables are. This makes our equation [tex]x=4y^3+8[/tex].
To find the inverse, we now need to solve for y in this equation.
[tex]x=4y^3+8[/tex] Subtract 8 from both sides:[tex]x-8 = 4y^3[/tex] [tex]4y^3 = x-8[/tex] Divide both sides by 4:[tex]y^3 = \frac{x-8}{4}[/tex] Take the cube root of each side: [tex]y = \sqrt[3]{\frac{x-8}{4}}[/tex] Convert into [tex]f^{-1}(x)[/tex] form [tex]f^{-1}(x) = \sqrt[3]{\frac{x-8}{4}}[/tex]Therefore, the inverse of this function is [tex]f^{-1}(x) = \sqrt[3]{\frac{x-8}{4}}[/tex].
Hope this helped!
Find the solution to the system. Write your solution as an ordered pair (x,y) with no spaces, no solution, or infinitely many. -6x+8y=12 and -3x+4y=6
Answer:
or infinitely manyStep-by-step explanation:
simplifying the equation -6x + 8y = 12 dividing by 2 would give us the same equation as
-6 / 2x + 8 / 2y = 12/2
-3x + 4y = 6
PLEASE PLEASE HELP ME I AM STUCK FIND ALL THE SOLUTIONS FOR X.
Answer:
Step-by-step explanation:
** SOLVE FOR N**
4n / 4 = 311 / 4
also please make sure it isnt a decimal
Answer:
Actual answer would be 77.75 but you would answer as 78 I believe.
Step-by-step explanation:
Since they're over the same denominator this means that 4n= 311.
311/4=n
n=77.75
Or for you it would be 78 rounded up.
Or for a fraction it would be 77 1/4.
(Thanks for reminding me)
Wilmer went up a hill for x minutes at a speed of y kilometers per minutes. Then he went down the same path at a speed of z kilometers per minute, and it took him w minutes to do it. Write an equation that relates x, y, z, and w. (The wording for this question really confuses me. And I do not understand which variable to put on it's own.) PLEASE ANSWER
Answer:
[tex]xy=wz[/tex]
Step-by-step explanation:
Given that:
Speed of Wilmer up the hill = [tex]y[/tex] km/min
Time taken up the hill = [tex]x[/tex] minutes
Speed of Wilmer down the hill = [tex]z[/tex] km/min
Time taken up the hill = [tex]w[/tex] minutes
Distance can be calculated by multiplying the Speed with Time i.e.
The formula for distance is given as:
[tex]Distance = Speed \times Time[/tex]
Distance up the hill = [tex]y\times x =xy\ kilometers[/tex]
Distance down the hill = [tex]z\times w =wz\ kilometers[/tex]
It is well known that, the distance up the hill and down the hill will be same.
Putting both the values equal, we get:
[tex]xy=wz[/tex]
Answer:
xy=wz
Step-by-step explanation:
please help pls and ty
9.2 Find the
Medn
of the following discrete
a x 20
90
SO
20
6
2
3
Answer:
Poorly formated. Please fix the question so it is more understandable!
What is 1 49/60 simplified? (fractions)
Answer: 109/60
Step-by-step explanation:
5x + 55= 2x+ 100
Please answer.
Answer:
x = 15
Step-by-step explanation:
Given
5x + 55 = 2x + 100 ( subtract 2x from, both sides )
3x + 55 = 100 ( subtract 55 from both sides )
3x = 45 ( divide both sides by 3 )
x = 15
A man pays Rs.1440 for income tax at the rate of Rs.2 per Rs.100. Find his income
Answer:
so 2 rupees tax for every 100rupees
we need to find how many 100's in 1440 and multiply with 2 so first divide 1440by 100 you will get 14.4 and multiply with 2 so the income tax is 28.8 you need to pay total 172.8.
Hope you understand if you understand give me a like
solve the system of equations.
Answer:
y=3, x=-1
Step-by-step explanation:
(2x+3y)-(2x-y)=7-(-5)
4y=12
y=3
2x+3y=7
2x=7-9
x=-1
PLS GIVE BRAINLIEST
Find the geometric mean of 3 and 48.
Answer:
12
Step-by-step explanation:
The point which divides the line segment joining the points (2, -6) and (3, 4) in the ratio 1 : 2 internally lies in the
1/2x +31/2y=
Please help I have only till 3 pm
Answer: [tex]\frac{x}{2}[/tex] + [tex]\frac{31y}{2}[/tex]
Step-by-step explanation:
1) Combine multiplied terms into a single fraction.
[tex]\frac{1}{2}[/tex] x + [tex]\frac{31}{2}[/tex] ⋅ y
2) Multiply the equation by 1.
1x/2+ 31/2 ⋅ y
x/2 + 31/2 ⋅ y
3) Combine multiplied terms into a single fraction.
x/2 + 31/2 y
x/2 + 31y/2
4) Solution
x/2 + 31y/2
The default horizontal alignment in Word is
A.centerd
B.justified
C.left aligned
d.right alined
KEABORDING SUBJECT
Answer:
i believe it is left aligned
Step-by-step explanation:
i hope it is correct if there is any wrong i will be glad to say for me :)
At the end of 5 years, how much money would you have in total if you invested $600 and earned 4% simple interest?
A $620
B $624
C. $720
D. $740
Answer:
720
Step-by-step explanation:
Sue makes bracelets. She uses
8
1
4
inches of chain to make one bracelet. How many bracelets can she make from a chain that is
49
1
2
inches long?
9514 1404 393
Answer:
6
Step-by-step explanation:
We estimate the number as 49/8 ≈ 6. We can check to see if this is too many by finding the chain required for 6 bracelets:
6 × 8 1/4 = 6×8 +6×1/4 = 48 +6/4 = 49 1/2
Sue can make 6 bracelets.
_____
You can also divide the total length of chain by the amount per bracelet:
(49 1/2)/(8 1/4) = (99/2)/(33/4)
= (99/2)(4/33) = (99/33)(4/2)
= (3)(2) = 6
Answer:
6
Step-by-step explanation:
We estimate the number as 49/8 ≈ 6. We can check to see if this is too many by finding the chain required for 6 bracelets:
6 × 8 1/4 = 6×8 +6×1/4 = 48 +6/4 = 49 1/2
Sue can make 6 bracelets.
_____
You can also divide the total length of chain by the amount per bracelet:
(49 1/2)/(8 1/4) = (99/2)/(33/4)
= (99/2)(4/33) = (99/33)(4/2)
= (3)(2) = 6
~ You're Welcome!! Asia
please help!! 15 points
Answer:
? = 125°
Step-by-step explanation:
The central angle is equal to the measure of the arc that subtends it, thus
? = 125°
Task: You and your friend were taking turns rolling a die when you thought of a game: If a one is rolled by either player, you pay your friend 50 cents, but when a different number is rolled, your friend pays you 10 cents. After 30 rolls, it turned out that you were even, and neither of you won anything.
Answer:
u both got rickrolled
Step-by-step explanation:
\_( XD)_/
Answer:
6 times
Step-by-step explanation:
'one' 50 cents, other 10 cents
If you get 50 cents you have to roll other number 5 times to minus 50 cents (50 divided by 10 is 5)
because they got nothing after roll so if they get a cents they have to minus it rolling other number
So if you divide 30 (the number of rolling) by 5 (the number of times to minus 50 cents) so the answer will be 6
Sorry this was too confusing
how to find the value of x in a triangle (5x-11)°, (2x+20)°, (11x-63)°
Answer:
x=13
Step-by-step explanation:
Well, the triangle is always equal to 180 degrees in total. Lets remember that x will always be the same in every equation.
So, (5x-11) x (2x+20) x (11x-63) = 180.
Now, take away the parenthesis and add up all the like terms.
This should = 18x-54 = 180.
Now solve like you regularly would. Add 54 on both sides which equals,
18x=234. Now, divide 18 on both sides.
x = 13.
Hope this helps.
f(x)=x²+2x-5 determine the vertex
Answer:
the point -5 is the vertex on the graph because it is the y-intercept.
Step-by-step explanation:
Answer:-16
dsfgdsggsgdsgsdg
Help? How do I do this.
3
What is the slope of the line y = 3x--?
4
so this equation is in y = mx + b form or slope intercept form
you can see that the slope is 3x since mx is slope
remember! m is always slope!
Amelia needs to buy some cat food. At the nearest store, 5 bags of cat food cost $26.25. How
much would Amelia spend on 6 bags of cat food
Answer:
$5.25
Step-by-step explanation:
Divide 26.25 by 5 and there's your answer.
Can someone help me plz thank you
Answer:The answer would be 43.75 so thank you :)
Step-by-step explanation:
Answer:
the total is $43.75 your welcome
pls halp
is the function even, odd, or neither and why
Answer:
ODD function
Step-by-step explanation:
Notice that there are two curves. Any point on one curve reflected through the origin is found on the other curve. In other words, the curves are symmetric with respect to the origin. Such curves typify ODD functions.
Answer my math question I asked so many times I lost most of points by
Answer:
i think ur in a higher grade then me but im good w/ equations so OoOO0p
Step-by-step explanation:
equation: y = x - 6 + x^2
(6,0) (7,1) (8,4) (9,9)
I figured this out by looking at the point (6,0). To get 0 (y), you have to subtract 6. Knowing this, I subtracted 6 from the rest of the coordinates, leaving me with numbers that are able to be squared to get y. This led me to the equation x - 6 + x^2.
!!!!!HELP WITH THIS ONE QUESTION PLEASE!!!!!
say wut in 30 secs and you will get 5o points and brain crown
Answer:
wut
Step-by-step explanation:
Please help will mark brainliest if correct
your brother has $200 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to find out how much he can spend on everything else.