Find a formula for the inverse of the following function, if possible.

[tex]P(x) = 3\sqrt[3]{x} - 1[/tex]

[tex]P^{-1}(x) = \\\\[/tex]

or does not have an inverse function

Answers

Answer 1

to find the inverse of any expression, we start off by doing a quick variables switcheroo and then solve for "y", so let's do so

[tex]\stackrel{P(x)}{y}~~=~~3\sqrt[3]{x}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ =~~3\sqrt[3]{y}-1}\implies x+1 = 3\sqrt[3]{y}\\\\\\\cfrac{x + 1}{3}=\sqrt[3]{y}\implies \left( \cfrac{x + 1}{3} \right)^3 =y\implies \cfrac{(x+1)^3}{3^3}=y\implies \cfrac{(x+1)^3}{27}=\stackrel{\stackrel{y}{\downarrow }}{P^{-1}(x)}[/tex]


Related Questions

will give 25 points if right

Answers

The slope of the equation is 1/6

Answer:

1/6

Step-by-step explanation:

When the equation is in the form "y = mx + b", m is the slope. This linear line has a slope of 1/6 and a y-intercept of -1/2.

Drag each relation to the correct location on the table. Classify the relations according to whether or not they are functions.

Answers

they are all functions

For any right triangle, the sum of the sqaures of the legs is equal to the square of the hypotenuse

Answers

Answer:

Pythagorean Theorem. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs of the right triangle. This same relationship is often used in the construction industry and is referred to as the 3-4-5 Rule.

figure b is a scaled copy of figure a

Answers

Step-by-step explanation:

figure B is a scaled copy of figure B

by scale factor : 1/2

2, 10 after a dilation by a scale factor of 1/2 centered at the
origin?

Answers

Answer:

  (1, 5)

Step-by-step explanation:

When the center is the origin, the dilation factor multiplies each coordinate:

  (2, 10) ⇒ (1/2)(2, 10) = (1, 5)

What is 162 multiplied by 0.967

Answers

The answer would be 156.654

Answer:

Remove the decimals and multiply normally.

162 x 967

156654

Put back in the decimals. In this case, move the decimal point back three spaces from the end.

156.654

:)

Where is the blue point on the number line ?

Answers

Answer:

-20

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

one period is 5, so -5×4 = -20

What is 64 minutes (1 hour and 4 minutes) as mixed number? I'm pretty sure its something like this:
[tex]1 \frac{?}{?} [/tex]
but I don't know for sure

Answers

Answer: 1  4/60

Step-by-step explanation

64 is greater then 60 . 60 = 1 hour so  64 minutes = 1 whole 4 over 60

Answer:

1 1/15.

Step-by-step explanation:

1 4/60

= 1 1/15.

Carly spent $150 on supplies and $125 on labor for her home. She could not spend more than $500 total. Which of these is a valid statement?

Answers

Answer:

she could spend up to $225 on more supplies

Step-by-step explanation:

the total amount of supplies and labor has to be less than or equal to $500. If she spent $150 and $125=$275 on supplies and labor, the equation would be 150+125+x≤ 500. Isolate x, to get x≤ $225. The value of x has to be less than or equal to $225.

Tutori
A decade ago, the average class size at Belmont Middle School was 30 students. Now it is
40% larger. What is the average class size currently?
PLS HELP

Answers

Answer:

42 students

Step-by-step explanation:

Initial class size = 30 students

Class size now is 40% larger:

30 + 40% = 30 + 30*40/100 = 30 + 12 = 42

First let's find larged amount

[tex]\\ \sf\longmapsto 40\%\:of\:30[/tex]

[tex]\\ \sf\longmapsto 0.4(30)[/tex]

[tex]\\ \sf\longmapsto 12[/tex]

Class size=30+12=42students

I REALLY NEED HELP CAN SOMEBODY PLZZZ HELP MEEEE

Answers

The mystery divisor is 18. I figured it out by dividing 4050 by 225.

In a right triangle, the measures of the legs are 8 and x + 6,
and the measure of the hypotenuse is x + 8. Find the value of x.

Answers

See the attached image for the steps.

x = 9.

Identities used :-

(a + b)² = a² + 2ab + b²

Theory used :-

Pythagorean theorem (Hypotenuse² = Base² + Altitude²).

______

RainbowSalt2222 ☔

Determine the intercepts of the line.
Do not round your answers.
y +5 = 2(x + 1)
y-intercept:
r-intercept:

Answers

Answer:

x intercept: (3/2, 0), y intercept: (0, -3)

Step-by-step explanation:

Abigail earned $10.26 for babysitting her cousin for 3 hours. How much did she earn in each hour?

Answers

Divide total earned by number of hours:

10.26/3 = $3.42

She earned $3.42 per hour

Each hour she earns $3.42

Describe a situation that could be represented
by 8

Answers

One student scored 92 percent in his math class. Another scored 100 percent in the same class.

By how much did the other student score higher than the first?

⇒ 8%

I hope this helps!

I need the answer ASAP please, 415 divided by 5

Answers

Answer:

83

Step-by-step explanation:

415/5

= 83

415 divided by 5 is 83.

pocket folders are $0.39 each at the store. If Carolyn paid $7.02, how many did she buy?

Answers

Answer:

18 pocket folders

Step-by-step explanation:

divide 7.02 by .39

Ms. McCullough bought a bunch of bananas. If she ate 2/8
the bananas and Mrs. Byrd ate 1/4, what fraction of bananas
remains?

Answers

Answer:

1/2

Step-by-step explanation:

that's the answer because 2/8-1/4 is 1/2

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicated that 35% plan to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 60 business owners. a. How many business owners in the survey plan to provide a holiday gift to their employees this year

Answers

The business owners that would provide a holiday gift to their employees this year is 21.

Percentage are a measure of frequency. It is the fraction of an amount that is usually expressed as a number out of hundred.

In order to determine the business owners that would provide a holiday gift to their employees this year, multiply the percentage of business owners that indicated they plan to give gifts by the total number of people surveyed.

35% x 60

0.35 x 60 = 21 people

To learn more about percentages, please check: https://brainly.com/question/92258

Select all ratios equivalent to 5:3.
13:9
9:15
20:12

Answers

Answer:

20:12

brainlest if it helped

Step-by-step explanation:

Answer:

20:12

Step-by-step explanation:

if you multiply 5:3 by 4, they'll end up with 20:12.

Should the United States return to a gold standard? Why?

Answers

Answer:

No

Step-by-step explanation:

If the U.S goes in a gold standard it can put the whole state in a crises

What is 3 4/5÷(−1 1/10)?

Write the answer as a mixed number in simplest form.

Answers

Step 1:(Not really helpful or important) I just follow the rules of BODMAS.B for bracket O for Of D for division M for multiplication A for addition and S small quiz in comment pls
I converted -11/10 to -1 1/10
Then I did 3 4/5 divided by it
Hope I help pls answer the quizzzz

100 POINTS ANSWER PLZ

On saturday endsay walked 3 1/2 miles in 1 2/5 hours what was her walking pace in miles per hour? write in somplest form

Answers

Answer:

2 1/2 mph

Step-by-step explanation:

Answer:

4 9/10

Step-by-step explanation:

trust me i tried posting a pic of my work but it wont load but it is 4  9/10

what is the area of the soccer field if x=40m?
base is 2x+20
height is x+20

Answers

2(40)+20 = 100m
40+20= 60m
100x60= 6000m

solve for x and y then find the measure of each angle ​

Answers

Step-by-step explanation:

∵ MP is a straight line.

∴ ∠MNQ + ∠PNQ = 180°

[tex](3y + 8)° + (3y + 22)° = 180° \\ 3y + 8 + 3y + 22 = 180 \\ 6y + 30 = 180 \\ 6y = 150 \\ y = 25[/tex]

∵ MP is a straight line.

∴ ∠MNR + ∠PNR = 180°

[tex](2x + 5)° + (3x - 55)° = 180° \\ 2x + 5 + 3x - 55 = 180 \\ 5x - 50 = 180 \\ 5x = 230 \\ x = 46[/tex]

help extremely quick plsssssssssssssssssssssssssssssssssss
Select all the expressions that have a value of 180 when b = 4.
A. 87b - 179 + 957 ÷87
B. 33b/12
C. b² + 120
D. 51b - 24
E. 11b + 187 - 2,756 ÷ 13

Answers

Answer:

A and E

Step-by-step explanation:

A 52-centimeter-long board is cut into 3 pieces. The longest piece is twice as long as the shortest piece. The other piece is 4 cm longer that the shortest piece. How long is each piece?

Answers

Answer:

4c 6th fastest 9.I gghiii

What is a common denominator for 1 3/4 and 1 4/5

Answers

Answer:

20

Step-by-step explanation:

A common denominator is a number that is a multiple of both denominators.

To find it just write the multiplication table of the numbers and find a number that appears in both of them.

In this case, we have 4 and 5:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40

5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Since it only asks for a common denominator, it can be 20, 40, 60, 80... Although it's usually smarter to pick the lower number.

[tex]1\dfrac 34 =1+ \dfrac 34 =\dfrac 74 = \dfrac{35}{20}\\\\\\1\dfrac 45 = 1+ \dfrac 45 = \dfrac 95 =\dfrac{36}{20}\\\\\text{The answer is 20}[/tex]

9.
Write the equation of the parabola in vertex form.



A. y = (x – 2)^2 + 4

B. y = x^2 – 4

C. y = (x – 2)^2

D. y = (x – 4)^2 – 4

Answers

Answer:   The Answer Is NOT Letter A

C. y = (x – 2)^2  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 2 , 0 )  =Already in vertex form.   y = ( x − 2 ) ^2

Step-by-step explanation:  I used math.way

A. y = (x – 2)^2 + 4  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 2 , 4 )  =Already in vertex form.   y = ( x − 2 ) ^2 + 4

B. y = x^2 – 4  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 0 , − 4 )  =Find the vertex form.   y = ( x + 0 ) ^2 − 4

C. y = (x – 2)^2  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 2 , 0 )  =Already in vertex form.   y = ( x − 2 ) ^2

D. y = (x – 4)^2 – 4  = Rewrite in vertex form and use this form to find the vertex  ( h , k ) .   ( 4 , − 4 )  =Already in vertex form.   y = ( x − 4 ) 2 − 4

It takes Shawn 4 more hours to stain a deck than Michelle. Together it takes them 4.8 hours to complete the work. How long would it take Shawn to stain the deck by​ himself?

Answers

Answer:

4.4 hours

Step-by-step explanation:

It would take Shawn 4.4 hours, as this would give a time of .4 hours to Michelle, totaling 4.8 hours

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