Mathematics High School

Let f be the function defined by f(x)=x^3+x^2+x. Let g(x)=f^-1(x), where g(3)=1. What is the value of g'(3)?

Answers

Answer 1

Answer:

1/6

Step-by-step explanation:

Given the function

f(x)=x^3+x^2+x

Get the inverse. Let y = f(x)

y = x^3+x^2+x

Replace y with x

x = y³+y²+y

Differentiate with respect to x

1 =3y²dy/dx + 2ydy/dx + dy/dx

1 = (3y²+2y+1)dy/dx

dy/dx = 1/3y²+2y+1

g'(x) = 1/3(g(x))²+2g(x)+1

If x = 3

g'(3) = 1/3(g(3))²+2g(3)+1

g'(3) =1/3(1)²+2(1)+1

g'(3) = 1/3+2+1

g'(3) = 1/6

Hence g'(3) = 1/6

Related Questions

please help


it due in a lil bit

Answers

The answer is D. You’re welcome.

Step by step: it’s asking you to find side BD, which is the adjacent to angle B.
And you know the opposite of angle B is AC or 3 inches.

This operation calls for TOA. T stands for Tan, OA stands for Opposite over Adjacent.
So we would do:
tan 60 = 3/x
And then next would be
x = 3/tan 60
Then, you probably have a calculator, so on a calculator do 3 divided by 60 and then press tan and press equal. You will get 1.73 which rounds to 1.7

Answer the following.
(a) A certain solution has a hydrogen ion concentration of 0.0000448 moles per liter. Write this number in scientific notation.

Answers

Answer:

35554555

Step-by-step explanation:

3(x^2-1) + 4(x^2 - 3) = 13

solve for x

Answers

Answer:

x=2, x=-2

Step-by-step explanation:

3x²-3+4x²-12=13

7x²=13+12+3

7x²=28

x²=4

x=-2

x=2

X =-2 should bring the correct answer

what is the equation of the following? Someone could help me to understand this? thank you​

Answers

Answer:

y=(1/5)x

Step-by-step explanation:

First, we must find the slope of the line.

The slope of a line can be found using the formula: (y2-y1)/(x2-x1)

(3-0)/(15-0)

(3)/(15)

1/5

The slope is 1/5.

Next we find the y-intercept, or where the line crosses the y-axis. In this case, the y-intercept is 0.

This gives us the equation: y=(1/5)x

Let me know if this helps!

Is 4( 3b - 4) equivalent to 2( 6b - 8) ?

Answers

Answer:

YES

Step-by-step explanation:

4(3b-4)=2(6b-8)

12b-16=12b-16

YES

Answer:

yes

Step-by-step explanation:

because 4*3=12 and 2*6=12 , and 4*4=16 and 2*8=16

helppp asap pleaseeeeee

Answers

The other answer is incomplete. The complete answers are B, C, and D

Can somebody help???

Answers

Answer:

first box - 2.10

second box - 2.14

Answer:

2.10 & 2.14

Step-by-step explanation:

its basic adding by 2 yk

The net of a triangular prism is show below.Find the rotal surface area of the triangular prism 4.6,4,5,15

Answers

Answer:

228.4cm²

Step-by-step explanation:

Find the diagram attached

Total surface area of the prism = Ph + 2B

P is the perimeter of the base (triangle)

h is the height of the prism

B is Base area

P = 5cm + 5cm + 4cm

P = 14cm

h = 15cm

B = 1/2 * base * height

B  = 1/2 * 4.6 * 4

B = 4.6 * 2

B = 9.2cm²

Substitute the values into the formula;

Total surface area of the prism = Ph + 2B

Total surface area of the prism = 14(15)+2(9.2)

Total surface area of the prism = 210 + 18.4

Total surface area of the prism = 228.4cm²

Hence the total surface area of the triangular prism is 228.4cm²

if 3x =9 what is x ?

Answers

Answer:

3

Step-by-step explanation:

All you have to do is divide 9 by 3 and you get 3!

I hope this helps, and have a great day! :)

the answer is 3 hope this helped

cuál es el resultado de 1/3 + 5/6?​

Answers

El resultado es 7/6

Answer:

it will be 1 1/6 or 7/6

Step-by-step explanation:

Hope this helped

help please, i don’t get this question .

Answers

Sales price is- $70
Tax on sale price is- $3.50
Final cost with discount and tax- $73.50

If the mLD = 3x - 8 and mZL = 2x + 17, find the
value of x that would make ZDE ZL.

Answers

Answer:

x = 25

Step-by-step explanation:

For ∠ D and ∠ L to be congruent, then

3x - 8 = 2x + 17 ( subtract 2x from both sides )

x - 8 = 17 ( add 8 to both sides )

x = 25

The midpoint of \overline{\text{AB}} AB is M(5, 1)M(5,1). If the coordinates of AA are (3, 6)(3,6), what are the coordinates of BB?

Answers

Answer:

(7, -4)

Step-by-step explanation:

The formula for calculating midpoint is expressed as;

M(X, Y) = (x2+x1)/2, (y1+y2)/2

X = x1+x2/2

Y = y1+y2/2

Given

X = 5, Y = 1, x1 = 3, y1 = 6

Get x2

X = x1+x2/2

5 = 3+x2/2

10 = 3+x2

x2 = 10-3

x2 = 7

Get y2;

Y = y1+y2/2

1 = 6+y2/2

2 = 6+y2

y2 = 2-6

y2 = -4

Hence the coordinate of B is at (7, -4)

Divide. Enter the quotient in simplest form.
9/10 divided by 3/8

Answers

12/5. ‍♀️‍♀️‍♀️‍♀️‍♀️‍❤️‍‍‍❤️‍‍

Find the value of x in the equation 2(x +1)=14

Answers

Answer:

the x=6

Step-by-step explanation:

2(6+1)=14

2(7)=14

14=14

x=6. the answer is 6

Kristin bought a snowboard for $60. The sales tax rate for the snowboard is $0.04 for every dollar spent. How much did Kristin pay in all for the snowboard?

Answers

62.4 dollars in total

Need help on this please help

Answers

Answer:

280m³

i hope this is help for you

The distance from your home to the school is 4 9/10 miles. From your house to the pool is 3 1/2 miles. How much farther are you from the school than from the pool?

Answers

4 9/10 - 3 1/2
4 9/10 - 3 5/10= 1 4/10 = 1 2/5 miles =1.4 miles
I agree with the person who answered first.

Help me I need the answer ASAP I’ll give brainliest

Answers

Answer:

number 2

Step-by-step explanation:

4/10 and 10/25 are equal : proportionate

pls help ;/ not hard btw




Simplify the following and write with positive exponents:

5z-5(3z)-2

Answers

Answer:

[tex] - 10z - 2[/tex]

Step-by-step explanation:

this is simplify

What 3.8in nearest tenth

Answers

Answer:

3.8

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Since the tenths place is where the 8 is 8 is over 5 and is closest to ten

The number of seeds found in a sample of 7 different oranges were: 3, 3, 4, 5, 7, 8, and 12. What is the range of the number of seeds in the sample of oranges?
A:5
B:6
C:7
D:9



PLz help me i need this answer

Answers

Answer:

9

Step-by-step explanation:

Range is Biggest Number - Smallest Number.

12 is the biggest number and 3 is the smallest number.

So, 12 - 3 = 9

Answer:

9

Step-by-step explanation:

becauses 12-3=9

hope it helps

Somone pls help if your good at math I’ll mark brainliest

Answers

ANSWER
(8,6)
STEP-BY-STEP

Answer:

x=5

Step-by-step explanation:

(x--3)²+(4--2)²=10²

(x+3)²+36=100

(x+3)²=64

(x+3)²=8²

x=5

i need help like really bad

Answers

Answer:

A

Step-by-step explanation:

14/15 is less than 7/5

Answer:

dang me too I'm like almost failing

Numbers 6 , 3 , (X – 4) are length of sides of an isosceles triangle , X =

Answers

For those question the anwser would be 5x+20=6 that was easy

A tree grows three feet per year. What happens to the growth of the tree when the number of years changes?
O When the number of years increases, the number of feet decreases.
O When the number of years decreases, the number of feet stays the same.
O When the number of years increases, the number of feet increases.
O When the number of years decreases, the number of feet increases.

Answers

Answer:

The tree will keep growing each year 3 feet.

Answer:

Your Answer is When the number of years increases, the number of feet increases

Tori has already jarred 1 liter of jam and will jar an additional 1 liter of jam every day. How
many days does Torì need to spend making jam if she wants to jar 10 liters of jam in all?

Answers

Answer:

9 days.

Step-by-step explanation:

We first subtract the amount already done from the total needed.

10 - 1 = 9.

Next, we take the remainder and divide it by the amount being made per day to get our final answer.

9 / 1 = 9.

The answer is 9 days.

Convert: 16 c =________gal

Answers

Answer:

16 cups is 1 gallon

Step-by-step explanation:

because there are 16 cups in a gallon

Find the maximum or minimum value of the graph below. Indicate whether it is a maximum or minimum value. ​

value=

a. -3
b. -1
c. 4
d. 1

Answers

c. 4 (it is a maximum since it’s the highest point on the graph)

This is my last 8th grade problem, again if you know the answer please interact :)

Answers

Answer:

same slope

parallel lines

Step-by-step explanation:

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