Find the inverse of the function f(x) = ^3 √x + 2 - 5
This image is the answer but I need the steps to how to solve it
Answers
The inverse function of the given function is
f ⁻¹(x) = x³ + 15x² + 75x + 123
What are inverse functions?
A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function f will take y to x if any function f takes x to y. When a function is written as f or F, its inverse is written as f⁻¹ or F⁻¹.
The given function is ∛(x+2) - 5
One of the properties of the inverse function is
f( f ⁻¹ x) = x
We utilise this property to find f ⁻¹ x.
f(x) = ∛(x+2) - 5
f( f ⁻¹x) = ∛( f ⁻¹(x) + 2) - 5
Using the above property
x = ∛( f ⁻¹(x) + 2) - 5
x + 5 = ∛( f ⁻¹(x) + 2)
Cubing both sides,
(x+5)³ = f ⁻¹(x) + 2
x³ + 15x² + 75x + 125 = f ⁻¹(x) + 2
f ⁻¹(x) = x³ + 15x² + 75x + 123
Therefore the inverse function of the given function is
f ⁻¹(x) = x³ + 15x² + 75x + 123
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Related Questions
a test to measure psychotic tendencies was given to a group of 1,000 potential air force cadets who wished to work in nuclear silos. any cadet who scored at or over 64 would be eliminated. the mean of the test was 52 and the standard deviation was 12. out of the 1,000 cadets how many were accepted?
Answers
840 of the 1,000 applicants were accepted to join the air force.
Explain the term psychotic tendencie?A mental health condition called psychosis makes people view or interpret the world in ways that are different from others around them. This could entail delusions or hallucinations.The given data:
Number of potential air force cadets n = 1000.mean = 52Standard deviation: 52 + 12 = 64Thus, selected cadets:
84% of 1,000
As, 84% is the percentile at one of the Standard deviation.
Thus, 840 of the 1,000 applicants were accepted to join the air force.
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(4) I'm stuck help me with how to get the equation show all ur steps
Answers
The number of solutions for the system of equations is given as follows:
Zero.
How to obtain the solution to the system of equations?The system of equations for this problem is defined as follows:
y = -5/3x + 2.5x + 3y = 12.We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
From the image presented at the end of the answer, the two graphs never intersect, and hence the number of solutions to the system of equations is of zero.
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Gabriel determined that his total cost would be represented by 2.5x 2y – 2. his sister states that the expression should be x x 0.5x y y – 2. who is correct? explain.
Answers
Answer:
Step-by-step explanation:
Hey! the answer is:
They are both correct, since the equations are the same.
I NEEEEEEED HELP ASAPPPPP!
Answers
Part 1:
The transformation performed from function f to function g are:
Function f is translated to the left 5 units
Function f is translated up to 1 unit.
Part 2:
The transformation performed from function f to function g are:
Function f is translated to the right 3 units
Function f is translated down to 4 units.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
We will use this concept:
f(x) = f(x - a) when translated a units to the right.
f(x) = f(x + a) when translated a units to the left.
Part 1:
f(x) = (x - 3)³ is tranform to g(x) = (x + 2)³ + 1
Now,
Translating f(x) with 5 units to the left.
f(x) = (x - 3 + 5)³
g(x) = (x + 2)³
Translating f(x) with 1 unit up.
g(x) = (x + 2)³ + 1
Part 2:
f(x) = ∛(x + 1) is tranform to f(x) = ∛(x - 2) - 4
Now,
Translating f(x) with 3 units to the right.
f(x) = ∛(x + 1 - 3)
f(x) = ∛(x - 2)
Translating f(x) with 4 units down.
f(x) = ∛(x - 2) - 4
Thus,
Part 1:
f(x) is translated with 5 units to the left and 1 unit up.
Part 2:
f(x) is translated with 3 units to the right and 4 units down.
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Solve for the value of pp (3p+6)° (4p+7)°
Answers
The value of the equation 6 + 3p = 4p + 7 is 1
How to solve the equation?Reorder the terms:
6 + 3p = 7 + 4p
Solving for the value of p by collecting like terms
6 + 3p = 7 + 4p
Move all terms containing p to the left, all other terms to the right.
Add '-4p' to each side of the equation.
-6 + 3p + -4p = -7 + 4p + -4p
Combine like terms: 3p + -4p = -1p
-6 + -1p = -7 + 4p + -4p
Combine like terms: 4p + -4p = 0
-6 + -1p = -7 + 0
-6 + -1p = -7
Add '6' to each side of the equation.
-6 + 6 + -1p = -7 + 6
Combine like terms: -6 + 6 = 0
0 + -1p = -7 + 6
-1p = -7 + 6
Combine like terms: -7 + 6 = -1
-1p = -1
Divide each side by '-1'.
p = 1
Simplifying
p = 1
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Rita goes to the mall. If d is the number of items she bought, the expression 18.82d+22 gives the amount she spent in dollars at one store. Then she spent 20 dollars at another store. Find the expression which represents the amount Rita spent at the mall. Then estimate how much Rita spent if she bought 6 items. PLEASEEEE HELPPPP
Answers
The expression which represents the amount Rita spent at the mall is 18.82d + 42. If d = 6, then the total amount spent is $154.92.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Amount spent at one store is given by the expression 18.82d + 22.
Here d is the number of items she bought at that store.
Amount spent at another store = $20
Total amount spent at the mall = 18.82d + 22 + 20 = 18.82d + 42.
If she bought 6 items, d = 6.
Total amount spent = (18.82 × 6) + 42 = $154.92
Hence the required expression to find the total amount is 18.82d + 42. And the total amount spent if the items bought is 6 is $154.92.
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portion of the population of interest that is selected for a study
Answers
The surveyor is interested in learning additional information about a segment of the general population. Numerous research projects call for particular interest groups to make decisions in light of their findings. This group of individuals is referred to as a sample.
What Exactly Is a Sample?
An easier-to-manage portion of a bigger group is referred to as a sample. It is a subset of individuals that shares traits with a wider population.
In statistical testing, samples are utilized when population sizes are too vast for all potential participants or observations to be included in the test.
What does a research sample mean?
Sampling is the process of choosing a portion of the target population for a research project.
In the vast majority of research projects, it is impossible to recruit the involvement of the entire population of interest, hence data gathering depends on a smaller group.
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a young boy gets into an accident with a parent. they get in a hospital in coma. the doctor looks at the patient and says i cant operate on the patient because thats my young boy. hows this possible? there is a building in the center of town. the building is 43 stories tall, and i am taller than that building. how is this possible? how is a raven like a writing desk?
Answers
This riddle does not have any mathematical formula or calculation associated with it.
This is an impossible situation, as it is not possible for a doctor to be the patient's parent. It is also not possible for a person to be taller than a building that is 43 stories tall.
The phrase "How is a raven like a writing desk?" is a riddle posed by Lewis Carroll in his novel Alice's Adventures in Wonderland. The answer to the riddle is "they both have the potential to produce a few notes, though they are very different". This phrase does not have any mathematical formula or calculation associated with it.
This riddle does not have any mathematical formula or calculation associated with it.
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11 ABCD is a quadrilateral.
Angle A = 60° and angle B=50°.
Calculate angles C and D.
60°
D
50%
C
B
Answers
Answer:
50 & 200
Step-by-step explanation:
The sum of all interior angles of a quadrilateral is 360 degrees, angle D is the same as B =50
angle C = 360-50-50-60 = 200
True or False?
Every rectangle with four congruent sides is a square.
Every rhombus is a quadrilateral.
Every square is a parallelogram.
Every quadrilateral is a square.
Answers
Every rectangle with four congruent sides is a square -> True
Every rhombus is a quadrilateral -> True
Every square is a parallelogram -> True
Every quadrilateral is a square -> False.
What is a square?A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
here, we have,
we know that,
Every rectangle with four congruent sides is a square -> True
Every rhombus is a quadrilateral -> True
Every square is a parallelogram -> True
Every quadrilateral is a square -> False.
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Help please on picture
Answers
The image of the translation 3 units right and 2 units down is attached.
What is transformation in geometry?Transformation in geometry is the process of changing the position, size, or shape of a geometric figure or shape. It can include
translations, rotations, reflections, and dilations,Translation in geometry is a transformation that involves moving a figure from one place to another on the coordinate plane, without changing its size or orientation.
The image of a figure after a translation is simply a slide of the original figure along the plane.
The translation involves adding 3 units to the x and subtracting 2 units to the y
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from a survey of 100 college students, a marketing research company found that 80 students owned ipods, 60 owned cars, and 50 owned both cars and ipods. (a) how many students owned either a car or an ipod (but not both)?
Answers
how many students owned either a car or an ipod (but not both): =100−90=10
What is union of sets?
Union of two given sets is the littlest set which contains every one of the components of both the sets.
What is intersection of sets?
Intersection of two given sets is the biggest set which contains every one of the components that are normal to both the sets
What is the recipe for union of two sets?
The union of two sets is given by
n(A∪B) = n(A) + n(B) - n(A∩B)
Where,
An and B are the two sets.
∪ is the union
∩ is the intersection.
n(AUB)=n(A)+n(B)−n(A∩B)
=80+60−50
=90
number of students owning a car or an ipod=90
number of students neither car nor stereo =100−90=10
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Twenty-five sixths times eight ninths
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the side length of square a is (2x 1) meters. the side length of square b is 2 meters longer than that of square a. find the difference in the area of the squares.
Answers
The difference in the area of the square 'a' and 'b' as per given side-length is equal to 8 ( x + 1 ) square meters.
Side length of square 'a' = (2x + 1) meters
Side length of square 'b' = ( 2x + 1 + 2 ) meters
= ( 2x + 3 ) meters
Area of a square 'a' = ( side length )²
= ( 2x + 1 )²
Area of a square 'b' = ( side length )²
= ( 2x +3 )²
Difference in the area of the squares = ( 2x +3 )² - ( 2x +1 )²
= ( 2x + 3 -2x -1 )( 2x + 3 + 2x + 1 )
= ( 2 ) ( 4x + 4 )
= 8 ( x + 1 )
Therefore, the difference in the area of the given squares is equal to 8 ( x + 1 ) square meters.
The side length of square 'a' is (2x + 1) meters. The side length of square 'b' is 2 meters longer than that of square a. find the difference in the area of the squares.
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Solve using the quadratic formula :
8x^2-4x+2=0
Answers
The solution of the given expression using the quadratic formula is x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16.
What is imaginary number?The complex numbers that are not real are represented by the fictitious unit "i." However, in order to convert complex numbers into their whole real form, we must first determine what the value of the fictitious number i is √-1.
Essentially, it was once thought that there was no difference between real and imaginary numbers in fact. Real numbers and fictitious numbers, however, were distinguished when the complex number entered the scene.
The quadratic formula is given as:
x = -b ± √ b² - 4ac ÷ 2a
In the given equation:
8x^2-4x+2=0
b = -4, a = 8, and c = 2
Substituting the value in the quadratic equation formula we have:
x = -(-4) ± √(-4)² - 4(8)(2) ÷ 2(8)
x = 4 ± √16 - 64 ÷ 16
x = 4 ± √-48 ÷ 16
The negative sign can be replaced by imaginary number (i)^2 hence:
x = 4 ± √48(i)² ÷ 16
x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16
Thus, the solution of the given expression using the quadratic formula is x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16.
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a six-lane urban freeway (three lanes in each direction) has a free-flow speed of 55 mi/h. traffic includes 10% trucks and 2% express buses. each truck and express bus displaces 2.0 passenger cars from the traffic stream. if the occupancy of passenger cars is 1.5 people per vehicle, and buses carry an average of 50 people per bus, what is the person-capacity of the freeway (in one direction)? it may be assumed that trucks carry one person (the driver).
Answers
The freeway can carry 85 vehicles per hour in one direction.
To calculate the person-capacity of the freeway in one direction, we can use the following formula:
Person-capacity = (Total number of vehicles - (Number of trucks + Number of buses)) × 2.0 × Occupancy × Speed
where,
Total number of vehicles = (Number of trucks + Number of buses) × 0.1
Therefore,
Person-capacity = ((Number of trucks + Number of buses) × 0.1 - (Number of trucks + Number of buses)) × 2.0 × 1.5 × 55 mi/hPerson-capacity = (Number of trucks + Number of buses) × 0.1 × 2.0 × 1.5 × 55 mi/hPerson-capacity = (Number of trucks + Number of buses) × 1.35 × 55 mi/hPerson-capacity = (Number of trucks + Number of buses) × 73.25 mi/hPerson-capacity = 85 people per hourIn conclusion, the freeway can carry 85 people per hour in one direction. This is determined by taking into account the freeway speed, the number of passenger cars, and their occupancy. We can plan accordingly by understanding the freeway's capacity with this calculation.
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asap pls help! it’s due in 5 mins
Answers
Answer:subtract to elimanate y
Step-by-step explanation:
What is the product 2/3 x 1/5
Answers
Answer: 2/15
Step-by-step explanation: First multiply the numerators together and then denominators together.
Numerators= 2 and 1
(numerators) 2 x 1 = 2
Denominators= 3 and 5
(denominators) 3 x 5 = 15
Hence, you get 2/15
Sophia owns a small business selling used books. She knows that in the last week 15 customers paid cash, 50 customers used a debit card, and 15 customers used a credit card. Based on these results, express the probability that the next customer will pay with a debit card as a decimal to the nearest hundredth.
Answers
The probability that the next person will pay with a debit card is:
P = 0.63
How to find the probability?
We want to find he probability that the next customer will pay with a debit card.
That probability can be estimated as the quotient between the number of customers that paid with debit card and the total number of customers.
We know that:
15 paid in cash.
50 paid with debit card.
15 paid with credit card.
For a total of 15 + 50 + 15 = 80
Then the probability is:
P = 50/80 = 0.63
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Ginny works at the local sneaker shop. She earns $17.50 per hour working there. Her boss offers her a promotion she can either receive a 12.5% hourly raise or $2.50 raise on her rate per hour. Ginny is not sure which choice will make her more money on a weekly basis.
Ginny chooses to take the 12.5% raise. She works 40 hours per week.
How much does she earn after 40 hours ?
Answers
Answer:
$787.5
Step-by-step explanation:
first, you have to find how much ginny makes in a week w/o her raise\
17.5*40=700
then, you have to raise it by 12.5%, so her new salary is 112.5% of 17.5
112.5% = 1.125
700*1.125=787.5
Area and Perimeter
If a = 5 in and b = 4 in, what is the area of the sketch?
OA. 139 in²
OB.
144 in²
OC. 101.5 in²
OD. 39.5 in²
2a
4b
Note: figure not drawn to scale
Reset
4
Submit
b
Answers
The total area of the shape is 165.5 in².
What is the area of the shape?
The total area of the shape is calculated from the area of the trapezium and the area of the base which is rectangle.
Area of the base ( rectangle ) = L x B
where;
L is the length = 4b = 4 x 4 in = 16 inB is the breadth = 2b = 2 x 4 in = 8 inArea of base = 16 in x 8 in = 128 in²
Area of the trapezium = ¹/₂ ( 2a + a ) a
= ¹/₂ ( 3a²)
= ¹/₂ ( 3 x 5²)
= 37.3 in²
Total area = 128 in² + 37.3 in² = 165.5 in²
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The diagonal of a tv screen is 26 inches. the base is 18.8 inches wide. how tall is the tv?
Answers
the height of the triangle formed by the diagonal and base of the TV screen.
The height of the TV is approximately 15.6 inches.
(26 inches / √2) = 18.8 inches
(18.8 inches * √2) = 26 inches
Height = (26 inches / 18.8 inches) * 18.8 inches
Height = 15.6 inches
Step 1: Calculate the hypotenuse of the triangle formed by the diagonal and base of the TV screen.
Hypotenuse = diagonal / √2
Hypotenuse = 26 inches / √2
Hypotenuse = 18.8 inches
Step 2: Calculate the diagonal of the triangle formed by the hypotenuse and base of the TV screen.
Diagonal = hypotenuse * √2
Diagonal = 18.8 inches * √2
Diagonal = 26 inches
Step 3: Calculate the height of the triangle formed by the diagonal and base of the TV screen.
Height = diagonal / base
Height = 26 inches / 18.8 inches
Height = 15.6 inches
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consider an experiment to investigate the effectiveness of different insecticides in controlling pests and their impact on the productivity of tomato plants. what is the best reason for randomly assigning treatments (spraying or not spraying) to the farms?
Answers
Randomly assigning treatments to the farms is the best way to ensure that the results of the experiment are valid, unbiased, and accurate.
Random assignment of treatments is the best way to ensure that the results of the experiment are valid and not biased. Random assignment of treatments would ensure that the results are not affected by factors such as soil type, climate, and other environmental conditions. This is because random assignment of treatments would ensure that the farms that receive the insecticide treatment are not systematically different from those that do not receive the treatment. This is important in order to gain accurate results from the experiment.
Random assignment of treatments is accomplished using the following formula:
Treatment Assignment = (Number of Farms) x (Random Number between 0 and 1)
By randomly assigning treatments to the farms, we can be sure that the results are not skewed by external factors. This will allow us to better determine the effectiveness of different insecticides in controlling pests and their impact on the productivity of tomato plants.
Randomly assigning treatments to the farms is the best way to ensure that the results of the experiment are valid, unbiased, and accurate.
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need help asap!!!
Match each expression on the left with an equivalent expression on the right. Not all of the options on the right will be used.
Answers
Answer:
100x14 = 1,400
14(10) = 140
361 * 1000 = 361,000
100(361) = 36,100
nine lines are drawn in a plane. what is the largest possible number of intersections in the plane which at least two of the nine lines intersect
Answers
The largest possible number of intersections in a plane with 9 lines is 36, which is achieved when each line intersects with every other line.
The largest possible number of intersections in the plane where at least two of the nine lines intersect is 36. To see why this is the case, consider a construction where each of the nine lines intersects with every other line. In this construction, each line intersects with eight other lines, so the total number of intersections is 9 * 8 / 2 = 36. This construction is possible to achieve in a plane, so 36 is the largest possible number of intersections.
This result can be explained using the formula for counting the number of intersections in a set of n lines. If each line intersects with every other line in the set, the total number of intersections will be equal to n choose 2, or n(n-1)/2, where n is the number of lines. In this case, n=9, so the maximum number of intersections is 9 choose 2 = 9(9-1)/2 = 36.
It is important to note that not all sets of nine lines in a plane will have 36 intersections. The actual number of intersections will depend on the specific configuration of the lines. However, 36 is the largest possible number of intersections for a set of nine lines in a plane.
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PLEASE HELP FOR 25 POINTS
Answers
The error interval for x when rounded to one decimal place as 8.7 is (8.65, 8.74).
What is rounding of values?The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
Here,
The rounded value of 8.7 is the midpoint of the error interval and any number between 8.65 and 8.74 would round to 8.7 when rounded to one decimal place.
Thus, the error interval for x when rounded to one decimal place is (8.65, 8.74).
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what are the differences between correlation and causation? how do organizations use linear regression. please give some examples. the output for linear regression analysis has multiple numbers. how can we interpret the output? share some hints.
Answers
Correlation does not imply causation, but in general, causality suggests correlation. In the corporate world, linear regressions can be used to analyze trends and provide estimates or hypotheses.
Although correlation suggests a relationship between variables, it does not prove that the covariation is due to a direct or causal link between them. However, causality implies a certain kind of link called a causal relationship, which is different from merely inferring a relationship (or circumstances and logical results relationship).
Linear regression is a very powerful measurable technique that may be used to develop experiences on customer behavior, acquiring clients, and factors impacting productivity. Additionally, linear regression can be used to examine an item's evaluation, sales growth, and advertising effectiveness.
The threat can be evaluated based on socioeconomic factors, vehicle characteristics, and driver information. Such an investigation could result in important business decisions being made as a result.
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PLEASE HELP ASAP!!! I'LL MARK BRAINLIEST TO RIGHT ANSWER!!!
Answers
The solution of the inequality is, x ∈ (- ∞, 5) ∪ (10, ∞)
Where, x represent the number of totts.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
My friend Raw has either no more than 5 toots and more than 10 toots.
Now, Let number of toots = x
Hence, We get;
⇒ x < 5
And, x > 10
Thus, The solution of the inequality is,
⇒ x ∈ (- ∞, 5) ∪ (10, ∞)
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in the final multiple score (fms), pass not advanced (pna) exam points are awarded for what maximum number of exam cycles? a) four
Answers
In the final multiple score (fms), pass not advanced (pna) exam points are awarded for five maximum number of exam cycles.
It is a calculation system, primarily practiced by the U.S Navy in order to make sure whether sailors in the pay grade of E-3, E-4, E-5 and E-6 are eligible in order to receive the position of the next pay grade. It consists of six categories such as exam score, performance mark average (PMA), etc.
If sailors score well, they will be awarded with PNA points. In each exam cycle, a sailor can receive a maximum of 3 PNA points, i.e., for a good score, 1.5 PNA points and for a good performance mark average, another 1.5 PNA points will be awarded.
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Complete question: in the final multiple score (fms), pass not advanced (pna) exam points are awarded for what maximum number of exam cycles? a) four, b) five, c) two, d) six
The moon orbits the earth at 384,400km. The distance from the earth to the sun is 149,600,00 km. The diameter of the sun is 1,391,000 km. What would the diameter of earth have to be to appear the same size as the sun from the moon?
Answers
The diameter of the Earth would need to be approximately 3,548.896 km to appear the same size as the Sun from the Moon.
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Let's call the diameter of the Earth "d".
From the Moon, the Earth is at a distance of 384,400 km,
and the Sun is at a distance of 149,600,000 km.
The ratio of the Sun's diameter to its distance from the Moon is
= 1,391,000 km / 149,600,000 km
= 0.00928.
So, to make the Earth appear the same size as the Sun, we need the ratio of the Earth's diameter to its distance from the Moon to be equal to 0.00928.
d / 384,400 km = 0.00928
Solving for d, we get:
d = 384,400 km x 0.00928
= 3,548.896 km
Hence, the diameter of earth should be 3,548.896 km
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