Mathematics College

f(x)=[tex]\sqrt{x^2-4}[/tex], x[tex]\leq \}[/tex]0

find [tex](f^-^1)'(1)[/tex]


I keep getting the wrong answer. The correct answer is[tex]\frac{1}{\sqrt{5} }[/tex]

Answers

Answer 1

Solve for x when √(x ² - 4) = 1 :

√(x ² - 4) = 1

x ² - 4 = 1

x ² = 5

x = ±√5

We're looking at x ≤ 0, so we take the negative square root, x = -√5.

This means f (-√5) = 1, or in terms of the inverse of f, we have f ⁻¹(1) = -√5.

Now apply the inverse function theorem:

If f(a) = b, then  (f ⁻¹)'(b) = 1 / f '(a).

We have

f(x) = √(x ² - 4)   →   f '(x) = x / √(x ² - 4)

So if a = -√5 and b = 1, we get

(f ⁻¹)'(1) = 1 / f ' (-√5)

(f ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5

The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of f at x = 1.

F(x)=[tex]\sqrt{x^2-4}[/tex], X[tex]\leq \}[/tex]0 Find [tex](f^-^1)'(1)[/tex]I Keep Getting The Wrong

Related Questions

I got a screenshot, You got answer

Answers

Answer:

A. [tex]V = (pi)(3.25)^2(12)[/tex]

Step-by-step explanation:

The formula for the volume of a cylinder is the formula for the area of the circle, times the height of the cylinder. The formula for the volume of a circle is,

[tex]A = (pi)(r)^2[/tex]

Multiply that by the height to find the formula for the volume of a cylinder,

[tex]V=(pi)(r)^2(h)[/tex]

Where (pi) represents the value (3.1415), (r) represents the radius, and (h) represents the height of the cylinder. Now substitute in the given values, remember, this problem gives the diameter of the cylinder, divide that value by two to find the radius.

[tex]V=(pi)(\frac{6.5}{2})^2(12)\\\\V = (pi)(3.25)^2(12)[/tex]

What is the answer I need to know

Answers

Answer:

Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

PLSSS HELP DUE IN 5 MINUTES!!!!
PLEASE DO NOT ANSWER JUST FOR POINTS!!!

LOOK AT THE IMAGE FOR THE QUESTIONS AND ANSWERS
NOTE: The first answer “(0,9)” is incorrect I tried and it was wrong so please it’s either (9,0) or (3,0)

Answers

Answer:

I think it's (0,3) sorry if it not

Answer:

(3, 0)

Step-by-step explanation:

The vertex point is 3 units to the right of the origin, making the x-coordinate 3, but it doesn’t move up or down, meaning that the y-coordinate is 0.

so it’s (3,0)

Btw, the vertex is the point of the parabola where it’s the minimum or maximu (minimum in this case). You answered for the y-interceptm which is where the parabola touches the y-axis.

What is the equation that represents the relationship shown in the table?​

Answers

The equation is x+8=y

Q. You're working in the sedan section of
Dean's Car Dealership. A customer makes a
down payment of 15% on a new car that costs
$13,450. How much is the down payment?
A. $201.75
B. $2,017.50
C. $269.00
D. $2,690.00

Answers

Answer:

B

Step-by-step explanation:

[tex]15%of$13,450=$2,017.50[/tex]%[tex]of13,450=2,017.50[/tex] therefore the down payment is $2,017.50

PLS HELP
Simply the expression by combining like terms.
6x+9+2x+4=

Answers

Answer:

Combine like terms: 18x + 15x = 33x

(45 + 33x + 6x2)

Step-by-step explanation:

Answer:

Combine like terms: 18x + 15x = 33x

(45 + 33x + 6x2)

Step-by-step explanation:

hello I need help to past this test on math:

(more than one answer)

Which of the following is part of the set of integers?

1. negative whole numbers
2. zero
3. natural numbers
4. positive whole numbers

what are the answers (more than one) 1,2,3,or 4?

(u dont need an explanation)

Answers

All of the choices (1 , 2 , 3 and 4) are correct

What is the area of the shaded region?

Answers

Area of a rectangle = length * width
So in this since, the area of the shaded area (which Is the whole rectangle)
A = 200ft * 100ft
A = 20,000

Answer:

17,680 ft²

Step-by-step explanation:

Shaded area = entire shaded rectangle area - unshaded rectangle area - square area

A = 200(100) - 24(30) - 40²

A = 20,000 - 720 - 1600 = 17,680

COULD SOMEONE HELP ME WITH C? I NEED TO TURN THIS IN ASAP

Answers

Answer:

I would, but unfortunately i don’t live in your brain. The question is asking for your opinion and what your prefer. Therefore, you have to answer which way is easier for you!

Good luck!

How many faces does the following shape have?

Answers

the shape has 4 faces . i hope this helps

Answer:

5

Step-by-step explanation:

the back ones 2

the front ones 2

and the bottom one 1

5

URGENT!!! WHOEVER GETS THIS CORRECT FIRST GETS BRAINLEST!!

Answers

Explanation:

I suggest using a calculator for this. The height is 4in, correct? And the width is 13in, correct? I suggest multiplying 13 and 4 together. if you got 52 then you are on the right track with this. The top and bottom of this perimeter is 13in each and the height on the left and right is 4in. 4 times 4 is 16. and 13 times 13 is 169. Sometimes people add 169 to 16 to get the answer but that is the wrong answer.

Answer:

The answer to this question is,

13 * 2 = 26

4 * 2 = 8

26 * 8 = 208

{-I apologize if i did the math wrong-}

Help fast please....

Answers

Answer:

46 yd²

Step-by-step explanation:

find the probability that a randomly selected point within the circle falls in the red shaded area round to the nearest hundredth r = 4 cm 2.5 cm 3 cm 3 cm

Answers

Answer:

[tex]p\approx 0.39[/tex]

Step-by-step explanation:

We are given a circle of radius 4 cm, and a triangle inscribed within the circle with a vertical height of 6.5 cm and a base of 6 cm.

To find the probability a randomly selected point lands in the red area, we can divide the red area by the total area.

The area for a circle is given by:

[tex]A=\pi r^2[/tex]

Since the radius is 4 cm, the area of the circle or total area is:

[tex]A=\pi (4)^2=16\pi \text{ cm}^2[/tex]

The area for a triangle is given by:

[tex]\displaystyle A=\frac{1}{2}bh[/tex]

The base of the triangle is 6 cm total and the vertical height is 6.5 cm. Therefore, the area is:

[tex]\displaystyle A=\frac{1}{2}(6)(6.5)=19.5\text{ cm}^2[/tex]

The probability of landing in the red shaded area is:

[tex]\displaystyle p=\frac{\text{Red Region}}{\text{Total Region}}[/tex]

Therefore:

[tex]\displaystyle p=\frac{19.5}{16\pi}\approx 0.39=39\%[/tex]

A rectangular prism has a volume of 240cm. It's height measures 8 cm. What is the area of its base

Answers

Answer: Base = 90 [tex]cm^{2}[/tex]

Step-by-step explanation:

A bowl of cold gazpacho soup is warming to room temperature. The temperature difference
between the soup and the room decreases by 5% every minute. What will the temperature
difference be in 8 minutes if it is currently 24°C?
If necessary, round your answer to the nearest tenth.

Answers

Answer: 25

Step-by-step explanation:

elana walked 12 miles. then she walked 1/4 that distance. how far did she walk all together. select all that apply.
12+1/4
12•1/4
12+1/4•12
12(1+1/4)
12•3/4
12•5/4

​

Answers

Answer:

12+1/4•12

Step-by-step explanation:

Hello friend!

The answer to your question is down below!!

1.  12+1/4•12

2. 12(1+1/4)

3.12+1/4

HELP ASAP PLZ DONT GUESS THIS DEPENDS ON MY LIFE FRR(graph in pic)

If Sheila rotates triangle PQR 90° counterclockwise to form triangle LMN, what is the measure of angle MNL?
A.130 °
B.100 °
C.50 °
D.30 °

Answers

Answer:

30

Step-by-step explanation:

This is a bit nasty, but you must keep the order in mind. PQR means that Q is the middle letter. M is also the middle letter. That's the easy part. What does MNL mean?

The lettering goes clockwise. MNL is the same thing as QRP. So what is R?

50 + 100 + R = 180

150 + R = 180

R = 180 - 150

R = 30

In the expression “six to the power
of four is 1,296," which number is the
base?

Answers

Six is the base because 6^4 is 1296.

A six-week fitness program was designed to decrease the time it takes retired individuals to walk one mile. At the beginning of the program, 20 randomly selected retired individuals were invited to participate, and their times to walk a mile were recorded. After the six-week program, their times to walk a mile were again recorded. Most participants saw little to no improvement in their times to walk one mile; however, a few participants saw drastic improvements in their times to walk one mile. The program director would like to perform a hypothesis test to determine if the program reduces the mean time for retired individuals to walk a mile. Which of the following statements is true?

a. Because there are 40 observations in total, the sample size is large enough to assume that the sampling distribution of the sample mean differences is approximately normal.
b. Because the walk times before and after the program are paired, a hypothesis test is not appropriate.
c. The sampling distribution of sample means can be assumed to be approximately normal because the distribution of the sample data is not skewed.
d. Because the sample size of 20 is less than 30 and the improvements in walk times in the sample data appear to be skewed, the distribution of sample means should not be assumed to be approximately normal.
e. Because the program recruited only retired individuals, the distribution of sample means should not be assumed to be approximately normal.

Answers

Answer:

c. The sampling distribution of the sample means can be assumed to be approximately normal because the distribution of the sample data is not skewed

Step-by-step explanation:

From the given data, we have;

The category of the sample = Retired individuals

The number of participants in the sample = 20

The duration of program = six-weeks

The improvement seen by most participants = Little to no improvement

The improvement seen by few participants = Drastic improvement

Therefore, given that the participants are randomly selected and the majority of the participants make the same observation of improvement in the time to walk a mile, we have that, the majority of the outcomes show little difference in walk times after the program, therefore, the distribution of the sample data is not skewed and can be assumed to be approximately normal

please hepl with this math

Answers

Answer:

3,10,17,24

Step-by-step explanation:

An Arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

3,10,17,24

the difference is 7

What if I fart instead of helping?

PLS HELP HELP ME WITH a question pls ​

Answers

Step-by-step explanation:

d.

e +e+25=180°{sum of angle of triangle}

2e+25=180°

2e=155

e=155/2

e=77.5°

e.

55°+55°+f=180°{sum of angle of triangle}

f=180-110

f=70°

hope it helps.

Calculator
Enter the unknown value that makes this statement true:
25% of O
is 30.
->
-
1
2
3

Answers

Answer:

X = 120

Step-by-step explanation:

here's your solution

=> we need to find the number whose 25%

is 30

=>. now , let the number be X

=> solve for X

=>. 25/100*X = 30

=> X = 30*100/25

=> X = 120

hope it helps

hey guys i need some help on this division problem i have

Answers

Answer:

3. 25/28

4. 1 1/7

Step-by-step explanation:

when you divide fractions just flip one of them and then multiply across

so instead of 5/7 ÷ 4/5 its

5/7 • 5/4

please mark me brainliest to help me get ace rank

divide 5/8 3/4 in the most simple form

Answers

Answer:

15/32

3/4 x 5/8 = 15/32 in fraction form.

Step-by-step explanation:

I need help with this !!!

Answers

Answer:

no it cannot be

Step-by-step explanation:

because :

2/10 equals to 10/2 So 6/10 ÷ 2/10 =6/10×10/2

6×10=60

10×2=20 after reducing the fraction its 3/1

look at the picture. please please help im stuck.​

Answers

Answer:

7 is greater than or equal to x.

Answer:

Hey I’m not sure but I think it’s A

Step-by-step explanation:

please help me with this :) thankss

Answers

Answer:

multiply all which would be 110  

Step-by-step explanation:

x−8<−1
Can someone plz tell me the answer

Answers

Answer:

Step-by-step explanation:

you have to add 8 in both sides

x-8<-1

x-8+8<-1+8

x<7

Answer:x<7

Step-by-step explanation:

Step 1: Add 8 to both sides.

x−8+8<−1+8

x<7

True or False.

The expressions 3+y and 13(6+y) are equivalent?



True

False

Answers

Answer:

False

Step-by-step explanation:

Brainliest please?

5 - 3(7n + 8) =??????????

Answers

Answer:

-21x-19

Step-by-step explanation:

Answer:

The answer is -19 - 21n

by the way in the image those are the letter N, I hope this helps you :)

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