Answers
Answer:
[tex]f^{-1}(x)=4x^2-3[/tex]
Step-by-step explanation:
The Inverse of a Function
Given a function f(x), the inverse of f, called [tex]f^{-1}(x)[/tex] is a function that satisfies:
[tex]f(f^{-1}(x))=x[/tex]
The domain of f becomes the range of its inverse and vice-versa.
The procedure to find the inverse of the function is:
* Write the function as a two-variable equation:
* Solve the equation for x.
* Swap the variables
We are given the function:
[tex]\displaystyle f(x)=-\frac{1}{2}\sqrt{x+3}[/tex]
Defined in the interval x ≥ -3
Note f is always negative, thus its range is f(x) ≤ 0
Now we find the inverse. Call y=f(x):
[tex]\displaystyle y=-\frac{1}{2}\sqrt{x+3}[/tex]
Multiplying by 2:
[tex]\displaystyle 2y=-\sqrt{x+3}[/tex]
Squaring both sides:
[tex]\displaystyle 4y^2=x+3[/tex]
Subtracting 3:
[tex]\displaystyle 4y^2-3=x[/tex]
Swapping variables:
[tex]y=4x^2-3[/tex]
Thus:
[tex]\mathbf{f^{-1}(x)=4x^2-3}[/tex]
The domain of the inverse is the range of f, thus x is restricted to
x ≤ 0
Related Questions
Question 1
Here is an inequality:
7x+6
2
< 3x + 2
Select all of the values that are a solution to the inequality.
Answers
Inequalities are used to relate unequal expressions
The values that are a solution to the inequality are: A. x = -3 and B. x = -2
The expression is given as:
[tex]\mathbf{7x + 6 < 3x + 2}[/tex]
Collect like terms
[tex]\mathbf{7x -3x < -6 + 2}[/tex]
[tex]\mathbf{4x < -4}[/tex]
Divide both sides by 4
[tex]\mathbf{x < -1}[/tex]
[tex]\mathbf{x < -1}[/tex] means that: the values of x are less than 1.
Hence, the values that are a solution to the inequality are: A. x = -3 and B. x = -2
Read more about inequalities at:
https://brainly.com/question/11612965
Cindy did an experiment. She started out with 600 bacteria cells. She found that the growth rate of the bacteria cells was 4.1%. Create an equation for the situation that would work for any time, x.
Pls Help thx
Answers
Answer:
Step-by-step explanation:
Hello! Im doing the same problem for my midterm and I believe the answer would be 0.041x+600.
Since x represents the time, x can be anything. 0.041 would equal the percentage of 4.1% and you need the growth rate times the time to equal your answer. +600 would be what she started out with, which is the bacteria cells. Hope this answers your question!!!
The graph shows the proportional relationship between the number of days and the total number of
hours driven. What is the constant of proportionality?
Answers
Answer:
twenty four is to sevev
please! im having trouble
Answers
Answer:
C. ∠K ≅ ∠R
Step-by-step explanation:
ΔJKL ~ ΔQRS
∠J ≅ ∠Q
∠K ≅ ∠R
∠L ≅ ∠S
9) Aunt Rosie made 50 pies for Mardi Gras.
She made 10 apple pies.
She made 12 pecan pies.
She made 8 chocolate cream pies.
What percent of the pies were pecan?
Answers
Answer:
25 percent
Step-by-step explanation:
Answer:
24%
Step-by-step explanation:
Use Percent equation (p = n w) or part of the whole = percentage times the whole
so we would have
12 = n 50
12/50 = n
0.24 = n
0.24 = 24%
Two sides of a triangle have lengths 5 and 15. Which expression describes the length of the third side? at least 10 and less than 20
at least 10 and less than 20
greater than 10 and less than 20
greater than 10 and at most most
at least 10 and at most 20
Answers
Answer: greater than 10 & less than 20
Step-by-step explanation:
someone pleaseeee help❤️
Answers
Answer:
106
Step-by-step explanation:
the angles combined equal 180 degrees. so to put it into an equation:
x+10+64=180
x+74=180
x=106
Step-by-step explanation:
All you do is add 10+64 which equals 74 the you subtract that from 180 then it is 106.
An elevator is on the tenth floor and drops 7 floors but then rises 12 floors. On what floor is the
elevator currently located?
a. 5TH floor b. 7TH floor
C. 12TH floor d. 15TH floor
Answers
Answer:
D. 15th floor
Step-by-step explanation:
10-7=3, 3+12=15
Find an expression for c that will make 9x2 + 12xy +c aperfect square trinomial
Answers
Answer: To find the value , divide the coefficient of by and square the result.
Step-by-step explanation:Use the formula ( b 2 ) 2 in order to create a new term in order to find the perfect square trinomial.
9 x 2 − 12 x + c + 4
who made up axillaries?
Answers
Answer:
Base: Formed by the skin that stretches from the arm to the thoracic cage; forms the indentation known as the axillary fossa. Anterior wall: Made up of the pectoralis major and minor, forming the anterior axillary fold.
copy and pasted but it helped me
Step-by-step explanation:
have a good day sir/ma'am
The table represents some points on the graph of a linear equation.What is the rate of change of y with respect to x for this function?
Answers
Answer:
Step-by-step explanation:
what we know=
x is the independent variable and y is the dependent variable.
our co-ordinates can be expressed in the form of (x value, y value).
so... we only need two points for this so let's just list two points so it goes faster
A(-7,5)
B(-1,65)
alright, now we have two points. we're trying to find the rate of change, which in other words, is the slope.
m=(y-y1)/(x-x1) <-- plug in our points.
m=(65-5)/(-1-(-7)
m=60/(-1+7)
m=60/6
m=10
therefore the rate of change aka the slope of this table of values is 10.
What is the slope of y = -1 + 3x?
What is the slope of y = -x + 7?
What is the slope of y = 3x + 8?
What is the y-intercept of the equation: y = 4x - 9?
What is the y-intercept of y = −3x − 2
Need this in 20 min
Do not spam!
I will report you if you spam!
Answers
Answer:
slope of y= -1+3x is "3"
of y=-x+7 is "-1"
of y=3x+8 is "3"
i) y intercept = "-9"
ii) y intercept = "-2"
help me lol plessssssss
Answers
Answer:
The answer is one
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
I first plugged 12 in for t in the equation:
5 - [tex]\frac{12}{3}[/tex]
I then used PEMDAS and solved [tex]\frac{12}{3}[/tex] , which is 4
That leaves you with 5-4 which is 1
-4-2/3x= -8
what is x?
Pls hurry I need help.
I will be posting a lot of math questions so once you answer this pls move onto the next one I post.
Answers
Answer:
x= 2/3
Step-by-step explanation:
here u go
Answer:
x= 6
Step-by-step explanation:
all you need is in the photo
Answers
Answer:
For the one that is in front of my right now the answer is (1,0) if you are asking for the interception point
Step-by-step explanation:
(x,y)
1 you need to move right one time to get the interception point and 0 times for going up or down so the equation will look like this:
(1,0)
Select the correct answer. Consider functions h and k. What is the value of ?
Answers
Answer:
Option (C)
Step-by-step explanation:
If two functions are f(x) and k(x),
(f o g)(x) = f[g(x)]
From the question given in the picture attached,
We have to find the value of (h o k)(1).
(h o k)(x) = h[k(x)]
= h[k(1)]
= h(3) [Since, k(1) = 3]
= 28 [Since, h(3) = 28]
Therefore, (h o k)(1) = 28 will be the answer.
Option (C) will be the correct option.
The correct option is C.
The calculation is as follows:
If two functions are f(x) and k(x),
(f o g)(x) = f[g(x)]
Now according to the picture
We have to find the value of (h o k)(1).
(h o k)(x) = h[k(x)]
= h[k(1)]
= h(3) [Since, k(1) = 3]
= 28 [Since, h(3) = 28]
Learn more: brainly.com/question/16911495
Lonnie rented a motorcycle for $40 plus $50 per mile that he rode.If his bill was $490, How many miles did he ride?
Answers
Answer:
he rode 9 miles
Step-by-step explanation:
490-40=450
450/50=9
Write the sentence as an equation.
301 multiplied by p is equal to 3
Answers
Answer:
301*p=3 or 301p=3
Step-by-step explanation:
Jaime hiked for 3 days across an island. He started at the shoreline, which is at an elevation of O feet.
• At the end of day 1, Jaime had gained 2,150 feet in elevation
. At the end of day 2, he had gained an additional 1,970 feet in elevation
On day 3, Jaime hiked down to the shoreline on the other side of the island, which is also at an elevation of O feet. How many feet in elevation did he lose on day 3?
A 1.970 feet
B
2,060 feet
С
2,150 feet
D
4.120 feet
Answers
Answer:
D. 4120 feetStep-by-step explanation:
Jamie lost on the third day:
2150 + 1970 = 4120 feetCorrect option is D.
answer
Step-by-step explanation:
2060 feet elevation did he loss on 3 days
Select the correct answer. What is the decimal equivalent of 10 ? ОА. 0.3 OB. 0.03 OC. 0.3 OD. 0.33 E. 0.003
Answers
3
What are the zeros or x-intercepts of the parabola?
A) (0, -1) and (0,5)
B (2,0) and (-9,0)
C (-1,0) and (5,0)
D (0,-5) and (-5,0)
Answers
Answer:
C
Step-by-step explanation:
x-intercepts , when y=0 are
(-1,0) and (5,0)
Answer:
C
Step-by-step explanation:
The zeros are also known as x-intercepts so it is the points on the x axis.
For x-intercepts the y is 0 so it is (-1,0) and (5,0)
hope this helped :)
Math problem HEEEELLLLPP
2(x+8)-2=897
Answers
Answer:
x = 883/2 or 441.5
Step-by-step explanation:
describe the transformation g(x)=f(x)+9
Answers
Answer:
f(x) has been translated to the left 9.
Step-by-step explanation:
The rule T(5,-3) is used for point (5,-1). Where is the translated point in the coordinate system
Answers
Answer:
Quadrant 4
Step-by-step explanation:
(5,-1), 5+5, -1-3 (10,-4) which is bottom left which is quadrant 4
The point (5, -1) is located in the fourth quadrant. Therefore, option B is the correct answer.
Given that, the rule T(5,-3) is used for point (5,-1).
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Quadrant rules:
First Quadrant: - x > 0 and y > 0. Thus, the sign of a point will be ( +, +).
Second Quadrant: - x < 0 and y > 0. Thus, the sign of a point will be ( -, +).
Third Quadrant: - x < 0 and y < 0. Thus, the sign of a point will be ( -, -).
Fourth Quadrant: - x > 0 and y < 0. Thus, the sign of a point will be ( +, -).
By studying above rules we understood (5, -1) in fourth quadrant.
The point (5, -1) is located in the fourth quadrant. Therefore, option B is the correct answer.
To learn more about the translation visit:
https://brainly.com/question/17485121.
#SPJ2
I'm on my sisters account and I'm in 4th grade my sis is in school help please
Answers
Your using ThinkCentral
Don't answer the question yet because I don't know if my answer is correct.
This is what I think you should do
3/4 x 2/1 ( I got the 2/1 from the other 3/4 ) = 3/2 or 1 1/2
I cross multiplied the 4 and the 2.
Hope my answer helps.
If you need 30 teaspoons of vanilla extract, how many ounces of vanilla do you need?5
If you need 30 teaspoons of vanilla extract and vanilla is sold in a 4 oz. bottle, how many bottles of vanilla should you buy?8
How much leftover vanilla will you have?
pls need help
Answers
what is the answer for this one 4x + 16 = ?
Answers
Answer:
4(x+4)
Step-by-step explanation:
Factor 4x+16
4x+16
=4(x+4)
Explanation: 4x + 16 = 24
4x + 16-16 = 24 -16
4x=8
4x/4=8/4
x=2
what Express 0.08 as a percent
Answers
Answer:
8%
Step-by-step explanation:
Solve the following equation for n:
8 + n = 16.
Answers
Answer:
n=8
Step-by-step explanation:
Answer:
n = 8
Step-by-step explanation:
8 + n = 16
Subtract 8 from both sides;
n = 8
Mofor and Eugene each improved their yards by planting hostas and ivy. They bought their
supplies from the same store. Mofor spent $208 on 14 hostas and 12 pots of ivy. Eugene spent
$152 on 13 hostas and 6 pots of ivy. Find the cost of one hosta and the cost of one pot of ivy.
Answers
ff
d
d
d
d
d
d
d
d
d
d
d
d
d
d
that’s the answer
