Inverse of the given function F(x) = 3 x³- 4 is F⁻¹(x) = ∛[ ( y + 4 ) / 3 ]
Given is a function of x, F(x) = 3 x³- 4
These question can be solved by following 4 easy steps
Step 1 : Switch the F(x) with the variable y
This implies, F(x) = 3 x³- 4 becomes y = 3 x³- 4
Step 2 : Interchange the variable x and y in the above obtained equation
This implies, from the equation y = 3 x³- 4, we get
x = 3 y³- 4
Step 3 : Solve the new obtained equation for y
This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.
x = 3 y³- 4
=> x + 4 = 3 y³
=> 3 y³ = x + 4
=> y³ = ( x + 4 ) / 3
=> y = ∛( x + 4 ) / 3
Hence we obtain the required equation.
Step 4 : Switch the variable y with F⁻¹(x)
This implies, y = ∛( x + 4 ) / 3 becomes F⁻¹(x) = ∛( x + 4 ) / 3
Therefore, we get the inverse of the given function F(x) = 3 x³- 4 as F⁻¹(x) = ∛( x + 4 ) / 3
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What is the function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the Y axis?
The function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the y axis is (x, y) ⇒ (x + 4, -y)
What is transformation?Transformation is the movement of a plane figure from one point to another. Transformation may also be an increase / decrease in the size of the figure. Examples of transformation are reflection, rotation, translation and dilation.
Dilation is the increase or decrease in size of a figure by a scale factor.
The function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the y axis is (x, y) ⇒ (x + 4, -y)
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whats the answer to this problem -10+7/4p=-38
Let's start by reviewing how to graph inequalities.
-5
-3
-2 -10
When the endpoint is a(n)
number represented by the endpoint
a part of the solution set.
3
dot or circle, the
When the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set.
What is a number line?A number line is a vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval
How to complete the blank statementFrom the number line in the question, we can see that:
The endpoint of the circle is an open circleThe arrow points to the rightAs a general rule, open circles implies that the number at that endpoint is not included part of the solution set.
Hence, the complete statement is "when the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set."
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What is the length of segment AB? (1 point) Coordinate grid shown from negative 8 to positive 8 on both x axis and y axis at intervals of 1. A straight line labeled AB is drawn. A is the ordered pair 0, 6 and B is the ordered pair 7, 0. a Square root of 13 b Square root of 85 c 13 d 14
The distance between points A and B is 9.22units, approximately.
This is further explained below.
What is the length of segment AB?Generally, In the image attached, you can observe a representation of the problem.
We have to find the distance between points A and B, which have coordinates (7,0) and (0,6), respectively.
The definition of distance between two given points is
[tex]d=\sqrt{\left(y_2-y_1\right)^2+\left(x_2-x_1\right)^2}[/tex]
Using points A and B, the distance between us
[tex]&d_{A B}=\sqrt{(7-0)^2+(0-6)^2}\\\\d_{A B}=\sqrt{49+36}\\\\\ d_{A B}=\sqrt{85} \\\\&d_{A B} \approx 9.22[/tex]
In conclusion, the distance between points A and Ais 9.22 units, approximately.
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Simplify each expression.
7¹/₂ . 21¹/₂
Express 7 and 21 as a product of their prime factors and write in index form.
The power rule states (a^m)^n = a^mn
7= 7^1
21 = 7x7x7 = 7^3 = 7^2 x7^1
(7^1)1/2 x (7^2x7^1)^1/2 = 7^1/2 x 7^2/2x7^1/2
7^1/2 x 7x7^1/2 = 7 x (7^1/2)^2
7x7 = 49
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If Sara completed her routine each day this week how many miles will she swim
Answer:
at least one mile for sure
if -5c+6 =-69 what is the value of 6c - 15
What is the image of the point (0, 9) after a rotation of 90° counterclockwise about
the origin?
Answer: -9,0
Step-by-step explanation:
Help please I don’t know what to do
Answer:
no
Step-by-step explanation:
half of 250k would be 125k and if you add that to 250k that would be 375k
Hello I will Mark Brainly Crown ! Its a Math question Please Help (geometry)
Thank you and please take care.
The sum of all exterior angles in any n-sided polygon is 360 degrees, so:
[tex]72 + 63 + 75 + x + 34 + 74 = 360 \\ x + 318 = 360 \\ x = 360 - 318 \\ x = 42[/tex]
What is the height, hhh, of the rectangular prism shown below?
Round your answer to the nearest tenth.
The height of the rectangular prism is 3 units.
What is rectangular prism?A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges.
Given:
Length(L)= 4 units
width(w)= 3 units
Diagonal(D) = [tex]\sqrt{34}[/tex] units
According to given question we have
The formula for rectangular prism is
[tex]L^{2} +w^{2} + h^{2} = D^{2} \\\\4^{2} +3^{2} +h^{2} =(\sqrt{34} )^{2} \\\\16+9+h^{2}=34\\\\25+h^{2}=34\\\\h^{2}=34-25\\\\h=\sqrt{9} \\\\h=3 units[/tex]
Therefore, the height of the rectangular prism is 3 units.
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Identify whether each cube root or square root lies between 2 and 3, 4 and 5, or 9 and 10
It should be noted that the square root and the cube root of the number has been attached.
How to illustrate the information?It should be here that the cube root of a number is the factor that we multiply by itself three times in order to get the original number.
It should be noted that thee symbol for cube root is 3✓ . Finding the cube root of a number is the opposite of cubing a number.
On the other hand, the square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.
It shouod be noted that for example, 4 and −4 are square roots of 16, because 4² = ² = 16.
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what if f(x)=3x+4 then f(n+3)=
Answer:
f(n + 3) = 3n + 13
Step-by-step explanation:
f(x)=3x+4 then f(n+3)=
f(n + 3) = 3(n + 3) + 4
f(n + 3) = 3n + 9 + 4
f(n + 3) = 3n + 13
I hope this helps!
D CONGRUENCE 3 Calculate the values of x, y and z in the triangle below. 3 cm 5 cm x cm- 4 cm 2 cm -ycm->
Answer:
Step-by-step explanation:
Solve each inequality.
||3x −1|+5| <1
The solution for the x for the inequality ||3x −1|+5| <1 is x<7/3
In the given problem basically, ||3x −1|+5| <1, we are dealing with the absolute value, which for real numbers is referred to as the non-negative value of that number without regard for consideration to its sign. Denoted by the symbol "| |', it is also known as the modulus of the number, and also with the inequality, which is a non-equal comparison between two numbers, additional mathematical expressions.
the inequality equation we got is ||3x-1|+5|<1
now we are taking the absolute value of it, we get
=>3x + 1 + 5 < 1
subtracting 1, and 5 from both sides, we get
=>3x < 1 + 5 + 1
=>3x < 7
=>x < 7/ 3
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You work for a wedding planner and have been asked to buy material for the table runners. Each runner is 4 feet long
and 8 inches wide. How much decorative material do you need, in square inches, for the top of each table runner?
32
40
64
120
384
Answer:
4*12=48
48*8=384
384 square inches
The mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by y = 3.50x + 6.00. explain how you can use this linear function to find out how many games you can bowl for $34.
The number of bowling games played for $34 is 8
The mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by linear equation y = 3.50x + 6.00
We are given that total money spent is $34
The number of bowling games played is assumed to be x
Now, we have substitute the value of y in the linear equation to get number of bowling games played
34 = 3.50x +6.00
34 - 6 = 3.50 x
28 = 3.5x
x = 28/ 3.5
x = 8
So, the number of bowling games played for $34 is 8
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What is 362584 rounded to the nearest thousand
1 unit left and 6 units up
The translated figure, 1 unit left and 6 units up, is given at the end of the answer.
What is the missing information?The original figure is missing, and is given at the end of the answer.
What is a transformation in a function?A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
The rule for a shift of 1 unit left and 6 units up is given as follows:
(x,y) -> (x - 1, y + 6).
The coordinates of the vertices of the original figure are given by:
(-7, -3), (-2,-4), (-7,-9), (-1,-9).
Hence the coordinates of the vertices of the translated figure are given by:
(-8, 3), (-3,2), (-8,-3), (0,-3).
The translated figure, 1 unit left and 6 units up, is given by the second graph at the end of the answer.
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three different angle in the diagram
Answer:
[tex] <por = x \: \: \: < ros = \beta \: \: \: pos = \gamma [/tex]
Find the inverse of each function. Is the inverse a function?
y=2 x-1
The inverse function returns the original value for which the output of a function was given.
The inverse the function y = 2x + 1 is [tex]y^{-1[/tex] = x + 1/ 2.
What is meant by inverse?Every logarithmic function has an exponential inverse, and vice versa.
An exponential function is a mathematical function with the formula f(x) = ax, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero.
The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.
Let the equation be y = 2x + 1
y = 2x + 1
simplifying the equation, we get
⇒ 2x = y+1
⇒ x = y+1/ 2
Therefore, the inverse is [tex]y^{-1[/tex] = x+1/ 2
Let the composition function be
[y ₀ [tex]y^{-1[/tex]] (x) = y (x+1/2)
simplifying the above equation
[y ₀ [tex]y^{-1[/tex]] (x) = 2 (x+1/2)-1
[y ₀ [tex]y^{-1[/tex]] (x) = x
The inverse of y is the image of y in the line y = x.
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A car rental company charges a rental fee of $45.
Additionally, they charge $15 per hour. How many hours will
it take for the total cost to be $105?
which one is right guys helppp
The linear equation of the graph is y = x - 5
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the linear equation?The graph represents the given parameter
On the graph, we have the following points
(x, y) = (1, -4) and (5, 0)
Calculate the slope (m) using
m = (y2 - y1)/(x2 - x1)
So, we have
m = (0 + 4)/(5 - 1)
Evaluate
m = 1
The equation is then calculated as
y = m(x - x1) + y1
So, we have
y = 1 * (x - 5) + 0
Evaluate
y = x - 5
Hence, the linear equation of the graph is y = x - 5
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A speed camera takes two phots of a car. photo 2 is taken 0.5 seconds after photo 1. marks on the road are 0.8 metres apart. calculate the average speed of the car in m/s
The average speed of car is 14.4 m/s.
We can see that from Photo 1 to Photo 2, the car covers 9 times the 0.8 meter distance. So, calculating the total distance traveled between the time span second photo was clicked.
Total distance traveled = 0.8×9
Performing multiplication
Total distance traveled = 7.2 meters
Now, the time is given as 0.5 seconds.
Finding the average speed using formula -
Average speed = total distance traveled ÷ total time taken
Keep the given values in formula to find the average speed.
Average speed = 7.2 ÷ 0.5
Performing division
Average speed = 14.4 m/s
Hence, the average speed of the car is 14.4 m/s
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The complete question is attached in figure.
7/10-?=7x10^? Pls I need answer asap thx
The complete representation of the expression is 7/ 10^-1 = 7 x 10^1
What are index forms?Index forms are simply defined as the exponent or power of a number raised to a variable or number.
It is known as the standard form of a number.
It is also known as the exponential representation of an expression or number .
Example;
The index form of 200 is 2 × 10^2
The index form of 40 is 4 × 10 ^1
Given the expression;
7/10- = 7x10^
We have;
7/ 10^-1 = 7 x 10^1
Thus, the complete representation of the expression is 7/ 10^-1 = 7 x 10^1
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Five buckets of water are needed to fill a fish aquarium. Each bucket hold 1.8 gallons. If one gallon = 3.8 L; how many liters will the aquarium hold?
23.6L
34.2L
2.36L
342L
Answer:
The answer is 34.2L
Step-by-step explanation:
5buc x 1.8gal = 9gal
9gal x 3.8L = 34.2L
A savings account begins with $ 14.00 . After 1 year, the account has a balance of $ 16.24 . After 2 years, the account has a balance of $ 18.84 . Assuming no additional deposits or withdraws are made, find the equation for the best-fitting exponential function to represent the balance of the account after x years. How much money will be in the account after 20 years?
The exponential function for to represent the balance of the account will be y = 14 ( 1.16) ˣ
We have that:
The saving account has initially = $ 14
After 1 year, the balance became = $ 16.24
After 2 years, the balance became = $ 18.84
Difference in the initial amount and amount after 1 year = $ 16.24 - $ 14 = $ 2.24
Difference in the amount after 1 year and amount after 2 years = $ 18.84 - $ 16.24 = $ 2.60.
An exponential function is defined as y = a ˣ where x is a variable, and a is a constant called the base of the function.
Here, the exponential function will be:
y = 14 ( 1.16) ˣ where x is the time period
Money after 20 years = 14 ( 1.16)²⁰ = $ 272.45
Therefore, we get that, the exponential function for to represent the balance of the account will be y = 14 ( 1.16) ˣ
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WILL GIVE BRAINLIESTTT
The graph of g(x) = -3(x-4)2 + 5 is translated 6 units left. What is the value of
h when the equation of the transformed graph is written in vertex form?
Step-by-step explanation:
the vertex form is
y = a(x - h)² + k
a is a stretch factor, (h, k) are the coordinates of the vertex of the parabola.
so, the original x-coordinate of the vertex was 4.
when we move it 6 units to the left. we subtract 6 from the x-coordinate.
that makes the new h
4 - 6 = -2
answer B is correct.
and the equation of the translated function is
g(x) = -3(x + 2)² + 5
mode of 75 55 68 44 82 28 19 31 75 36 59 93 48
Answer:
75
Step-by-step explanation:
In math, mode is the number which appears most in the data set. When dealing with this, first put all of the numbers in numerical order, least to greatest.
19, 28, 31, 36, 44, 48, 55, 59, 68, 75, 75, 82, 93
Notice how 75 appear twice and all the other numbers appear once. Therefore the mode is 75.
5004300 in standard form
Answer:
5004300
Step-by-step explanation:
This number is already in standard form, but I can help if you want it in scientific notation, etc.