Find the inverse of the function f(x) = 2x^3 - 5


This is what I have so far
F(x) = 2x^3 - 5
Y = 2x^3 - 5
X = 2y^3 - 5
+5 +5
x + 5 = 2y^3

Answers

Answer 1

9514 1404 393

Answer:

  f^-1(x) = ∛((x +5)/2)

Step-by-step explanation:

Continue to solve for y.

  [tex]x +5=2y^3\qquad\text{so far so good}\\\\\dfrac{x+5}{2}=y^3\qquad\text{divide by 2}\\\\\sqrt[3]{\dfrac{x+5}{2}}=y\qquad\text{take the cube root}\\\\\boxed{f^{-1}(x)=\sqrt[3]{\dfrac{x+5}{2}}}\qquad\text{expressed in functional form}[/tex]

If you want to "rationalize the denominator", you can multiply both numerator and denominator by 4 inside the radical. This will simplify to ...

  [tex]\displaystyle\boxed{f^{-1}(x)=\frac{1}{2}\sqrt[3]{4x+20}}[/tex]

Answer 2
y be f(x)

[tex]\\ \rm\Rrightarrow y=2x^3-5[/tex]

Interchange y and x

[tex]\\ \rm\Rrightarrow x=2y^3-5[/tex]

[tex]\\ \rm\Rrightarrow 2y^3=x+5[/tex]

Isolate y

[tex]\\ \rm\Rrightarrow y^3=\dfrac{x+5}{2}[/tex]

[tex]\\ \rm\Rrightarrow y=\sqrt[3]{\dfrac{x+5}{2}}[/tex]

This is the inverse

[tex]\\ \rm\Rrightarrow f^{-1}(x)=\sqrt[3]{\dfrac{x+5}{2}}[/tex]


Related Questions

What is the value of sin _ in the diagram below? Please help bro

Answers

Answer:

sinΘ= 24/25

Step-by-step explanation:

The sine of the coordinate point is the y value.

What is 3/4 X 4/3 in lowest term? *
a. 1
b. 3/4
c. 7/12
d. 4/3​

Answers

3/4 x 4/3 is 12/12 which is also simplified to 1.

Answer:

A. 1

Step-by-step explanation:

When multiplying fractions, you multiply across. 3/4*4/3 would be 12/12 because 3*4 is 12 and 4*3 is 12. 12/12 is the same thing as 1.

Hope this helps!

PLEASE SHOW YOUR WORK Solve for 3^3 + 14y - (25y - 13) = y + 7y - 9y

Answers

Answer:

Step-by-step explanation:

2.1     Factoring  9y2+30y-14

The first term is,  9y2  its coefficient is  9 .

The middle term is,  +30y  its coefficient is  30 .

The last term, "the constant", is  -14

Step-1 : Multiply the coefficient of the first term by the constant   9 • -14 = -126

Step-2 : Find two factors of  -126  whose sum equals the coefficient of the middle term, which is   30 .

     -126    +    1    =    -125

     -63    +    2    =    -61

     -42    +    3    =    -39

     -21    +    6    =    -15

     -18    +    7    =    -11

     -14    +    9    =    -5

     -9    +    14    =    5

     -7    +    18    =    11

     -6    +    21    =    15

     -3    +    42    =    39

     -2    +    63    =    61

     -1    +    126    =    125

4. Geoff and Gina bought 20 books altogether. If Geoff gave 6 of his books to Gina, the number of books he had would be 2 fewer than the number of book Gina had. How many books did each of them buy?​

Answers

Answer:

f#*k

Step-by-step explanation:

gfsgfdruerrrrrs

6x+6y=7 solve for slope

Answers

Answer:

m = -1

slope = -1

Step-by-step explanation:

Mr. Keen buys a wagon that was originally priced at $130 and then reduced by 10%. What was the reduced price?​

Answers

10% of 130 is 13
130-13=
Final answer: 117

Answer:

117

Step-by-step explanation:

10%130 = 13

130-17= 117

Just put that in the calculator tbh

What is 64% of 85?
Want to show steps

Answers

Answer:

54.4

Step-by-step explanation:

64% is 0.64 in decimal form. So, you just simply multipy 0.64 by 85 to get 54.4.

Consider x=10-y complete the table for the equation

Answers

Step-by-step explanation:

Given equation ,

=> x = 10 - y

When x = 0

=> y = 10 - x

=> y = 10 -0 = 10

===========================================

When x = 1

=> y = 10 -1 = 9

===========================================

When x = 2

=> y = 10-2 = 8

Answer:

(0, 10), (1,9), (2,8)

Step-by-step explanation:

Substitute your x values and solve for y.

0=10-y (Subtract 10)

-10=-y (Divide by -1)

10=y

1=10-y (Subtract 10)

-9=y (Divide by -1)

9=y

2=10-y (Subtract 10)

-8=y (Divide by -1)

8=y

Hopefully, this helps :)

Rewrite the equation below so that it does not have fractions.
2/9x-5=2/3

Answers

I would think it would be 0.22x-5=0.66. Al you have to do it take a calculator and do 2 divided by 3 for the first fraction. The second fraction would just be 2 divided by 3!

A package of 3 pairs of insulated socks cost $27.37 what’s the unit price of the pairs of socks

Answers

$9.12


27.37 divided by 3 = 9.12333….

Simplified it would equal 9.12

Hope this helps :)

Kyle's school is 2.34 mi from his house. One day, he rode his bike 2.5 times that distance
Which choice is the closest estimate of the number of miles Kyle rode his bike?

Answers

Answer: About or Around 5.85

Step-by-step explanation:

All you do is times 2.34 times 2.5 and you get 5.85

I couldn't work this out on here because I don't know how to get it on the way I want it.

when somebody says why you like me what should i say

Answers

Answer:

Not even related to math. But say no.... Unless you really like them then say yes

Step-by-step explanation:

Evaluate the equation −12/c=6

Answers

Answer:

-2

Step-by-step explanation:

First you want to seperate the c. To do that you divide by both sides so -12/c divide -12 cancels out to be just 1/C. 6 divide -12 is -0.5. Know we have 1/c = -0.5 and that is -2. -2 is your answer :)

how to surpass the whole class​

Answers

Work Hard and poop on em

Can someone help my please I need to do this fast

Answers

Answer:

1 and 4

Step-by-step explanation:

Answer:

(-3, 8)

Step-by-step explanation:

[tex]7x-14y=-133\\35x+14y=7[/tex]

[tex]42x=-126[/tex]

[tex]x=-126/42=-3[/tex]

[tex]5(-3)+2y=1\\-15+2y=1[/tex]

[tex]2y=1+15\\2y=16\\y=16/2=8[/tex]

I hope this help you

Plz help I need help

Answers

Answer:

yes they show a relationship which is a linear relationship

Step-by-step explanation:

for x values it's n=x+1 while n represents and for y values it's n=y+1

Answer:

The answer is 3

Step-by-step explanation:

2+3=5

3+3=6

4+3=7

5+3=8

Which function is the inverse of ƒ(x) = 4x3 – 2?

Answers

Answer:

[tex]\sqrt[3]{\frac{x+2}{4}}[/tex]

Step-by-step explanation:

how do you round 9372282 to the nearest 1000

Answers

Answer:

9372000

Step-by-step explanation:

9372282 rounds to 9372000

Since we're rounding to the thousand, we need to look at the number in the hundreds place, in this case it's 2 (9372282). 2 is lower than 5, so we round down. If it was 5 or higher, we'd round up. Rounding down means, we just keep the other 2 as a 2 (9372282), and change the numbers after to 0s (9372000)  

How does the range of g (x) = StartFraction 6 Over x EndFraction compare with the range of the parent function f (x) = StartFraction 1 Over x EndFraction?

Answers

Answer:

The range of both f(x) and g(x) all nonzero are real numbers.

Step-by-step explanation:

I think is an answer choice so is B.

:)

Luis posee un terreno y va a colocar un cerco de forma rectangular con una malla 80 metros de longitud. Para ello ha establecido dos objetivos:

•Utilizar toda la malla (los 80 metros).
•La superficie que desea cercar debe ser la máxima posible.

Si "x" e "y" representan las dimensiones del terreno.
a) ¿Cuál es la función qué relaciona las dimensiones del terreno?
b) ¿Cuál seria la función qué relaciona el área del terreno con dimensiones?
c) Representa en el plano cartesiano la función relaciona el área del terreno con una de sus dimensiones
d) ¿Cuánto debe medir el ancho y el largo del terreno para que el área sea la máxima posible? Justifica tu respuesta​

Answers

Queremos resolver distintas cosas en relación a las dimensiones de un rectangulo, las respuestas son:

a) 80m = 2*(x + y)

b) A = (40m - y)*y = 40m*y - y^2

c) El grafico se puede ver al final de la respuesta.

d) Tanto el largo como el ancho deben ser iguales a 20m

Luis quiere colocar un cerco rectangular, definamos, x como el largo e y como el ancho de este rectangulo.

Recordar que el area está dada por:

A = x*y

y el perimetro está dado por:

P = 2*(x + y)

Ahora sabemos que el desea utilizar una malla de 80 metros de longitud, es decir, el perimetro debe ser:

P = 80m = 2*(x + y)

Ahora tenemos una ecuación que relaciona las dimensions del terreno.

a) 80m = 2*(x + y)

b) La ecuación del area es:

A = x*y

Usando la ecuación del inciso (a) podemos escribir:

80m = 2*(x + y)

40m = x + y

x = 40m - y

Ahora podemos reemplazar esto en la ecuación del area:

A = (40m - y)*y = 40m*y - y^2

c) El grafico se puede ver al final de la respuesta.

d) Queremos maximizar el area.

Notar que la ecuación del area es cuadratica, es decir, el máximo esta en el vertice, y el vertice está dado por:

y = -40m/(2*-1) = 20m

Usando la ecuación x = 40m - y podemos encontrar el valor de x:

x = 40m - y = 40m - 20m = 20m

Es decir, el largo y el ancho deben ser iguales a 20 metros.

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Hana bought a house two years ago costing £210,000. House prices in her region are expected to increase by 2.3% per year, correct to two significant figures.

Calculate the minimum expected value of her house now

Answers

Answer:

=219 660

Step-by-step explanation:

Its 2.3 per year and the question says 2 years ago so 2.3×2

=4.6%

So,

210 000÷100×4.6

=9660

now

9660+210000

=219 660

HOPE ITS HELPS GIVE BRAINLIEST!

Answer:

210.000÷2.3% is answer is 215.000

Step-by-step explanation:

beccause the 2.3% is 5.000 per month


please that can answer this will get 50 points and I'll mark BRAINLIEST.
plot the graph of y= 2cos2x-1 ranging from 0°<x<180°. Use 2cm rep 30° on x axis and 2cm rep 1 unit on y axis. (a) On the same axis plot the graph of y=(1/180)(x-360 ) (b) use the graph to solve the equation 2cos2x-(x/180)+1=0. (c) Find the values of of x for which for which 2cos2x+(1/2)=0. (please a step by step explanation)​

Answers

y=2cos^2x-1

Graph attached

A survey is conducted to collect information about tour preference. 100 interviewees are asked to choose
from ‘River Cruise’, ‘Shopping tour’ or ‘Eco Trip’ as the main activity for the last day of a tour. Below is
the result of the survey:
Male Female
River Cruise 20 , 14
Shopping Tour 15 , 36
Eco Trip 11 , 4
(a) Find the probability that an interviewee chooses ‘Eco Trip’.
(b) Find the probability that a male interviewee chooses ’Shopping Tour’.
(c) In the group of interviewees choosing ‘Shopping Tour’, find the proportion of female.
(d) An interviewee does not choose “River Cruise”. What is the probability that this person is a female?
(e) May is one of the female interviewees in this survey. She does not choose “Eco Trip”. What is the
probability that she chooses “River Cruise”?

Answers

Using the probability concept, it is found that:

a) There is a 0.1485 = 14.85% probability that an interviewee chooses ‘Eco Trip’.

b) There is a 0.3261 = 32.61% probability that a male interviewee chooses ’Shopping Tour’.

c) The proportion of females is of 0.7059 = 70.59%.

d) There is a 0.6061 = 60.61% probability that this person is a female.

e) There is a 0.3953 = 39.53% probability that she chooses “River Cruise”.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item a:

Total of 20 + 14 + 15 + 36 + 11 + 5 = 101 interviewees.11 + 4 = 15 choose Eco Trip.

Hence:

[tex]p = \frac{15}{101} = 0.1485[/tex]

0.1485 = 14.85% probability that an interviewee chooses ‘Eco Trip’.

Item b:

20 + 15 + 11 = 46 male interviewees, 15 choose Shopping Tour, hence:

[tex]p = \frac{15}{46} = 0.3261[/tex]

0.3261 = 32.61% probability that a male interviewee chooses ’Shopping Tour’.

Item c:

15 + 36 = 51 interviewees choose Shopping Tour, 36 are female, hence:

[tex]p = \frac{36}{51} = 0.7059[/tex]

The proportion of females is of 0.7059 = 70.59%.

Item d:

15 + 36 + 11 + 4 = 66 interviewees do not choose River Cruise, 36 + 4 = 40 are female, hence:

[tex]p = \frac{40}{66} = 0.6061[/tex]

0.6061 = 60.61% probability that this person is a female.

Item e:

101 - 15 = 86 people do not choose Eco Trip, of those, 34 choose River Cruise, hence:

[tex]p = \frac{34}{86} = 0.3953[/tex]

0.3953 = 39.53% probability that she chooses “River Cruise”.

A similar problem is given at https://brainly.com/question/24944430

easy question................

Answers

Answer:

3.80

Step-by-step explanation:

there are ten points starting after 3 on the line, count them

Answer:

3.80

Step-by-step explanation:

Which expressions are equivalent to

4(3e+2)+9(e+4)+1 ?

Select all that apply.

3 (7e +15)

16e +45

45 + 21e

3 (7e +45)

6+2 (5e +20) + 5

Answers

Answer:

45 + 21e   3  (7e  +15)

Step-by-step explanation:

The equivalent expression of the expression 4(3e+2) + 9(e+4) + 1 will be

⇒ 45 + 21e

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 4(3e+2) + 9(e+4) + 1

Now,

We can simplify the expression as;

⇒ 4(3e+2) + 9(e+4) + 1

⇒ 12e + 8 + 9e + 36 + 1

⇒ 21e + 45

⇒ 45 + 21e

Thus, The equivalent expression of the expression 4(3e+2) + 9(e+4) + 1 will be;

⇒ 45 + 21e

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Plz help I need help

Answers

Answer :

x + 23 = -22

• x = -22 - 23

• x = - ( 22 + 23 )

• x = -45

x = -45 ✔️

x + 23 = -22

x = -22 - 23

x = -(22+23)

x = -45

Rectangle ABCD is dilated by a scale factor of 2 with the origin as the center of dilation, resulting in the image A'BCD. If the slope of AB Is-2,
what is the slope of A' B'?

Answers

Answer:

C. -2

Step-by-step explanation:

A (x,y)   B(x',y')      slope of AB = (y'-y)/(x'-x) = -2

After dilation with factor of 2:

A' (2x,2y)     B' (2x',2y')   slope of A'B' = (2y'-2y)/(2x'-2x) = (y'-y)/(x'-x) = -2

The slope of A' B' is the same as the slope of AB, which is -2.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The slope of line AB is -2, and the slope of A' B' can be found by applying the transformation to the slope of AB.

Since the dilation is centered at the origin and has a scale factor of 2, the slope of line A' B' is also -2.

This is because the transformation multiplies the distances between points by 2 in every direction, but it does not change the angle between the lines.

Therefore, the slope of A' B' is the same as the slope of AB, which is -2.

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Use the decimals 3.91, 8.41, and 45 to write two different addition facts and two different subtraction
facts.

Answers

                                                                                                                  ur math class is even a young on’ could have solved this, you can literally look it up on gogle, your just giving out fre point at this “point.” No pun “intent”ed. Ok I should stop

Multiply and simplify the product. (3 – 5i)(–2 + 4i) Select the product. 14+ 2i 14 + 22i 15 + 22i 26 + 2i

Answers

Answer:

I got -6 + 2i

Step-by-step explanation:

(3-5i)(-2+4i)

So we would multiply the following:

3*-2 = -6

3*4i =12i

-5i*-2 = 10i

-5i * 4i = -20i

Therefore the expression would be

- 6 + 12i + 10i - 20i

we then would add and subtract the variables, which would be

-6 + 2i

I hope this helps! Have a nice day!

I Need Help Fast??
25=​

Answers

The answer is 5

This is because 5x5=25
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