Answers
Step-by-step explanation:
f^-1 means the inverse function that finds the x responsible for the creation of a given y (functional result) value.
y = 3x - 1
3x = y + 1
x = 1/3(y + 1)
and now we rename x to y and y to x, so that we get a normal function definition :
y = 1/3(x + 1) = (1/3)x + 1/3
now we create the first derivative d/dx of this function :
y' = 1/3
since both f(x) and f^‐1(x) are line functions with a constant slope, it is not surprising that the first derivative (the function of the slope of the base function) is a constant function.
so, for any value of x (incl. the requested x = 11) d/dx f^-1(x) = 1/3.
therefore also d/dx f^-1(11) = 1/3.
y = 2×sqrt(x)
sqrt(x) = y/2
x = y²/4
again we rename the variables, so that we get a normal function definition for the inverse function :
y = x²/4
the first derivative is :
y' = 2x/4 = x/2
so, d/dx f^-1(6) = 6/2 = 3
Use the inverse function theorem: if f(x) is continuously differentiable at x = a, and given f(a) = b, then f is invertible around x = a, and
[tex]\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}[/tex]
Both the given functions f(x) meet the conditions above. Note that you don't need to actually compute the inverse function itself.
If f(x) = 3x - 1, then f(x) = 11 when
3x - 1 = 11 ⇒ 3x = 12 ⇒ x = 4
Now if f(4) = 11, it follows from the inverse function theorem that
[tex]\left(f^{-1}\right)'(11) = \dfrac1{f'(4)} = \boxed{\dfrac13}[/tex]
since f'(x) = 3.
If f(x) = 2√x, then f(x) = 6 when
2√x = 6 ⇒ √x = 3 ⇒ x = ±9
But note that f(x) is defined only for x ≥ 0, so we must take x = 9. Now if f(9) = 6, the inverse function theorem says
[tex]\left(f^{-1}\right)'(6) = \dfrac1{f'(9)} = \dfrac1{\frac1{\sqrt9}} = \boxed{3}[/tex]
since f'(x) = 1/√x.
Related Questions
1. Subtract the linear expressions.
(45x−5)−(13x+4)
What is the difference?
Enter your answer in the box. Enter fractions as simplified fractions.
2. Add the two expressions.
−2.4n−3 and −7.8n+2
Enter your answer in the box.
3. Subtract the linear expressions.
(−3.6x+9.4)−(1.9x+3.6)
What is the difference?
Enter your answer in the box.
4. Subtract 5x−2 from −3x+4 .
A.2x + 2
B.8x−6
C.−8x+6
D.−8x+2
Please try and put the correct answers.
If all correct I will mark them brainilest
Answers
[tex](1)\\\\(45x -5) -(13x +4) = 45x-5-13x -4 = 32x -9\\\\\\(2)\\\\-2(4n) -3 + (-7)(8n) +2 = -8n-56n -1 = -64n -1 = -(64n+1)\\\\(3)\\\\(-3.6x+9.4) - (1.9x +3.6) = -3.6x +9.4 -1.9x -3.6 =-5.5x+5.8\\\\\\(4)\\\\-3x+4-(5x-2) = -3x+4-5x +2=-8x +6[/tex]
Solve the slope for this table.
Answers
Answer:
-1/3
Step-by-step explanation:
as x increases by 3, y decreases by 1, so the slope is y/x= -1/3
Write 0.00000506 in scientific notation.
Answers
Answer:
5.06*10 to the power of -6
Step-by-step explanation:
you need the number to be in between one and 10 so 5.06 is where the decimal should be and the exponent is negative because when you want to put it back to the rational number you go 6 decimal places to the LEFT
Roy bought a drum set for $422 and a guitar E La
for $358. If sales tax is 7.5%, what is the total
a free
cost of the instruments, including tax?
The in
amour
Answers
Answer:
The final total including tax is 838.5
The sale tax is 58.5
Step-by-step explanation:
60 out of 300=?
I’m not sure how to figure that out
Answers
Answer:
60 / 300 simplified 6/30 simplified 1/5 (20%)
Step-by-step explanation:
Maybe asking ratio?
Convert 32 feet per second to kilometers per hour. (Hint: There are 5280 feet in a mile, and one mile is 1.61 kilometers)
Step by Step please
Answers
Answer:
35.113 km per hour is the correct answer
Plz solve. I will give 50 points for whoever gets it right.
Answers
Answer:
This is like multiplication you solve this question and then you can solve the equation
please help for brainlist you need to be accurate tho
Answers
Answer:
3.5t +5
Step-by-step explanation:
We are looking for the total distance
5 miles is the first distance traveled.
Then after the break they travel at a rate of 3.5 miles per hour for t hours
That distance is 3.5t
The total distance traveled is
5+3.5t
Rewriting the order
3.5t +5
can someone give me the answer no explaining
Answers
Answer:
Greater than
Step-by-step explanation:
Answer:
5/3 is greater
Step-by-step explanation:
Round 53,714.54 to the nearest a. thousandth. b. thousand.
Answers
help..................
Answers
Answer:
Line A
Step-by-step explanation:
please help!!!!!!!!!!
Answers
Answer:
120 / (x+y) = 8
Step-by-step explanation:
120 / (x+y)
= 120 / (3+12)
= 120/15
= 8
What’s pemdas and how do we use it ?
Answers
Answer:
pemdas is an order of operation
Step-by-step explanation:
PEMDAS STANDS FOR parentheis, exponents, multiplication, division, addition, and subtraction. it is the order of how you should solve multi step equations EXAMPLE: 1+2x2 FIRST you have to multiply the 2x2 because multiplication comes first in PEMDAS, then you do the addition so 2x2=4+1=5
PEMDAS is the order that you solve a problem.
PEMDAS stands for:
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction
If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.
In the equation
2 + 3 * 5,
first you would do 3 * 5 because multiplication is before addition.
2 + 15
Then you would do the addition to get the answer:
17.
Please give brainliest
Pls help thank you for those who put hard work
Answers
Step-by-step explanation:
given,
a = 18
given expression,
a + 8
a/q
18 + 8 = 26
therefore, correct answer is 26.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
35is what percent of 25
Answers
Answer: 140
Explanation: 35/25 = 1.4 = 140%
Would appreciate brainly <3
Answer:
Percentage Calculator: 35 is what percent of 25? = 140.
Step-by-step explanation:
hehe :)
At Keller's Bike Rentals, it costs $36 to rent a bike for 7 hours.
How many hours of bike use does a customer get per dollar
Answers
Answer:
I'm sure it's 43 rent a bike cause I'm fat
How to find standard deviation from true probability and sample size.
Answers
Answer:
I can even see anything can you reupload your answer, please?
Step-by-step explanation:
A store sells 4 cans of soup for $9. How much would it cost you to buy 5 cans of soup?
Answers
Answer:
$11.25
Step-by-step explanation:
4 x 5 = 20
9 x 5 = 45
20/4 = 5
45/5 = 11.25
A helicopter floats 120m above a helipad, a dog is 85m from the helipad, if the dog could fly, how far would it have to fly to get to helicopter?
Answers
If the dog could fly, it would need to fly 147 meters to catch the helicopter
This is a rather easy and straightforward question. We are going to solve it using Pythagoras theorem. We can interpret the question to be in a triangle where the height of the helicopter above the helipad and away from the dog is the right angle. This also means that the distance needed, between the dog and the helicopter is the hypotenuse.
Using pythagoras theorem, we have
120² + 85² = c²
c² = 14400 + 7225
c² = 21625
c = [tex]\sqrt{21625}[/tex]
c = ±147 meters.
Since distance cant be in the negative, our answer is 147 m
read more about pythagoras theorem here https://brainly.com/question/15138986
Solve the literal equation for x.
k= nx - 3x
Answers
answer:X=k/n-3
explain:move all terms to the left side and set equal to zero. then set each factor equ to zero!
I hope this helps
k/(n-3)=x
there ya gooooo
14. Find the area of this rectangle.
Answers
Answer:
8×7 = 56 cm^2
.....................
Answer:
Step-by-step explanation:
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
so
8 × 7 = 56 cm²
A number c minus 7.3 is less than 6. write this word sentence as an inequality?
Answers
Answer:
c - 7.3 < 6
Step-by-step explanation:
c - 7.3 is less than 6
less than is the same as <
So c - 7.3 < 6
-Chetan K
Answer:
c - 7.3 < 6
Step-by-step explanation:
The ratio of roses to tulips is 2:3. What percent of the flowers are roses?
Answers
Answer:
40%
Step-by-step explanation:
Roses are 2/(2+3) = 2/5 = 2/5×100% = 40% of the total.
A farmer owns 70 acres of land. Of the 70 acres, only 65% can be farmed. How many acres are available for farming? acres are available for farming. How many are not available for farming? acres are not available for farming.
Answers
45.5 acres of land can be farmed and 24.5 cannot be farmed.
I wmat to sleep been doing work for an hour help me out
Answers
Answer:
A. 23, 37.....
B. 26, 42......
Step-by-step explanation:
have a great day!
Ten times the sum of a number and 12 is 84.
Answers
Answer:
12×10 = 120
NOT 84
THE ANSWER IS 120
what are all the common factors of 15, 45, and 90?
and what are all the factors of 15, 45 and 90?
Answers
The factors of 45 are: 1, 3, 5, 9, 15, 45
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Common factors are: 1 3 5 15
expand and simplify (x+3)²
Answers
Answer:
x² + 9 + 6xStep-by-step explanation:
expand and simplify (x+3)²
(x+3)² =
x² + 9 + 2 × x × 3 =
x² + 9 + 6x
Answer:
x² + 6x + 9
Step-by-step explanation:
( x + 3 ) ²
( x + 3 ) ( x + 3 )
x ( x + 3 ) + 3 ( x + 3 )
x² + 3x + 3x + 9
x² + 6x + 9
Hope this helps you.
Let me know if you have any other questions :-)
a boy is y years old now .how old was he 10 years ago
Answers
Answer:
Hi there the answer is y-10
A company sells three types of gift baskets. The basic basket has two movie passes and one package of microwave popcorn, and costs $15.50. The medium basket has two movie passes, two packages of microwave popcorn, and one DVD, and costs $37. The super basket has four movie passes, three packages of microwave popcorn, and two DVDs, and costs $72.50.
Create a system of equations and solve using matrices to find the price of each basket item.
Answers
The price of each movie is $7, the price of each microwave popcorn is $1.50 and the price of each DVD is $20.
Let x represent the cost of each movie, y represent the cost each microwave and z represent the cost of each DVD.
For the basic:
2x + y = 15.50 (1)
For medium:
2x + 2y + z = 37 (2)
For super:
4x + 3y + 2z = 72.50 (3)
[tex]\left[\begin{array}{ccc}2&1&0\\2&2&1\\4&3&2\end{array}\right] \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}15.5&37&72.5\end{array}\right] \\\\\\ \left[\begin{array}{c}x&y&z\end{array}\right] =\left[\begin{array}{ccc}2&1&0\\2&2&1\\4&3&2\end{array}\right]^{-1}\left[\begin{array}{c}15.5&37&72.5\end{array}\right]\\\\\\ \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}7&1.5&20\end{array}\right] =[/tex]
The price of each movie is $7, the price of each microwave popcorn is $1.50 and the price of each DVD is $20.
Find out more at: https://brainly.com/question/21105092