Find the inverse of the function, no solutions doesn't work and things like sqrt(9-x^2) doesn't either.
Answers
Answer:
The range of [tex]f(x)[/tex] is [tex]f(x)\in[0,3][/tex]
[tex]f^{-1}(x)=-\sqrt{-x^2+9}[/tex] with a domain [tex]x\in[0,3][/tex]
Step-by-step explanation:
Domain: set of input values (x-values)
Range: set of output values (y-values)
Given function:
[tex]f(x)=\sqrt{9-x^2}\quad(x\in[-3,0])[/tex]
Therefore, as the original function has a restricted domain, its range is also restricted:
[tex]f(-3)=\sqrt{9-(-3)^2}=0[/tex]
[tex]f(0)=\sqrt{9-0}=3[/tex]
[tex]\therefore\textsf{Range}\:f(x)\in[0,3][/tex]
To determine the inverse of a function
Change [tex]x[/tex] to [tex]y[/tex]:
[tex]\implies x=\sqrt{9-y^2}[/tex]
Square both sides:
[tex]\implies x^2=9-y^2[/tex]
Switch sides:
[tex]\implies 9-y^2=x^2[/tex]
Subtract 9 from both sides:
[tex]\implies -y^2=x^2-9[/tex]
Divide both sides by -1:
[tex]\implies y^2=-x^2+9[/tex]
Therefore:
[tex]\implies y=\sqrt{-x^2+9}\textsf{ and }y=-\sqrt{-x^2+9}[/tex]
As the range of the inverse function is the same as the domain of the original function:
[tex]\implies f^{-1}(x)=-\sqrt{-x^2+9}[/tex] only as the range is [-3, 0]
The domain of the inverse function is the same as the range of the original function.
[tex]\therefore\textsf{Domain of}\:f^{-1}(x):x \in [0,3][/tex]
The inverse of a function is ordinarily the reflection of the original function in the line [tex]y=x[/tex].
**Please see attached graph**
Related Questions
Solve this linear system using determinants:
2x + 3y = 6
- 8x - 3y = 12
A=
Az =
[Ayl =
Answers
2×+3y=6
-8×-3y=12
-6×=18
×=18/-6
×=-3
——————
2×+3y=6
2(3)+3y=6
6+3y=6
3y=6-6
3y=0
Y=0/3
Y=0
——————
×=3
Y=0
————
2×+3y=6
2(3)+3(0)=6
6=6
xLasersx✨A rectangle has an area of 227.9m^2.
One of the sides is 5.3m in length.
Work out the perimeter of the rectangle.
Answers
Divide the area by the side length to find the length of the other side:
227.9/5.3 = 43 m
now calculate the perimeter:
43 + 43 + 5.3 + 5.3 = 96.6m
Answer: 96.6m
Answer:
96.6 m
Step-by-step explanation:
Let the length of the other side b x m .
Then the area = 5.3 * x
227.9 = 5.3x
x = 227.9 / 5.3
= 43 m
So the perimeter = 2 * (width + length)
= 2(5.3 + 43)
= 2 * 48.3
= 96.6 m
Solve this QUICKLY and explain, please
Answers
Answer:
Step-by-step explanation:
c
so you have to combine like terms so subtract 8 - 4 and the 4 disappears so it be like this
8 - 2x = 4 + x
-4 -2x = -4 + x
4 - 2x = x
next combine the like terms of the 2x so
4 - 2x = x
4 + 2x = +2x
4 = 2x
now you divide 4 by 2 so like this
4 = 2x
2 2
and your answer is x = 2 try to solve the other one if you need help ask me
Find the area of the quadrilateral
Answers
Answer:
58.58
Step-by-step explanation:
[tex] \frac{1}{2} \times 10 \times 3 \\ 5 \times 3 = 15.....(1)[/tex]
[tex] \frac{1}{2} \times 10 \times 10 \\ 5 \times 10 = 50...(2)[/tex]
Add one and two :- 15+ 50 = 65
Please help with one through three Brainliest to the correct in best answer
Answers
Answer:
1. Alike
2. Opposite
3. Common factor
Step-by-step explanation:
1. To have a positive number, you can only have alike signs, for example, any positive number times another positive number is always positive. The same is true for negative numbers multiplied by each other.
2. To have a negative number, there has to be one negative number and one positive number being multiplied together. Always. For example:
3 x -5 =-15
10 x -1 = -10
3. You can factor out a common factor to simplify a polynomial before you factor it.
Tanya is training for a bike race. She rode ten miles on Monday, twelve miles on Wednesday, seventeen miles on Thursday, and thirty one miles on Saturday. How many miles in all did Tanya ride?
Answers
Step-by-step explanation:
in total Tayna rides 70 miles.
Savage growth of human hair is 0.5 in per month find how long it takes a human to grow 3 inches of hair for a human
Answers
Find the value of X round your number to the nearest tenths
Explain it please
Answers
In this case, we must use trigonometry to find the value of x:
[tex]tan(\alpha )=\frac{side-opposite-angle}{side-beside-angle} \\tan(70) = \frac{x}{3} \\3*tan(70) = x\\x = 3*tan(70)\\x = 8.24[/tex]
Thus the value of x rounded to the nearest tenth is 8.2
Hope that helps!
What are quadratic equations? What are some examples?
Answers
Answer:Examples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc. From these examples, you can note that, some quadratic equations lack the term “c” and “bx.”
Step-by-step explanation:
A quadratic equation in the variable x is an equation of the form ax^2 + b x + c = 0, where a, b, c are real numbers, a ≠ 0.
What are quadratic equations?Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.
The standard form of a quadratic equation is;
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c where a, b, c, ∈ R and a ≠ 0.
These are the following examples of the quadratic equation;
x^2-2x
x^2+5x+6
x^2-5x
Any equation of the form p (x) = 0, where p (x) is a polynomial of degree 2, is a quadratic equation.
If we write the terms of p (x) in decreasing order of their degrees, then we get the standard form of the equation.
Learn more about quadratic equations here;
https://brainly.com/question/2263981
#SPJ4
A rectangle has an area of 73.5m2 one of the sides are 1.5m in length work out the perimeter of the rectangle
Answers
Answer:
101m
Step-by-step explanation:
area of a rectangle is given by length × width
73.5÷1.5 gives us the other side=49
49+1.5=50.5×2=101
9/5 - (-6/10)
Khan academy needs either exact fraction or exact decimal
Answers
Answer:
Exact fraction: 6/5
Exact Decimal: 1.2
Answer:
12/5 = 2.4
Step-by-step explanation:
The fraction 6/10 can be reduced to simplify the addition.
9/5 -(-6/10) = 9/5 +6/10 = 9/5 +3/5
= 12/5 = 2.4
__
The two minus signs "cancel." The product of any set of numbers with an even number of minus signs will be positive.
These are the values in Irwin’s data set.
(1, 43), (3, 36), (5,22), (6, 25), (8,14)
Irwin determined the equation of a linear regression line, and determined that these are the predicted values.
(1, 44), (3, 35), (5,26), (6, 22), (8,13)
Use the point tool to graph the residual plot for the data set.
Answers
The residual points include the difference between the value in Irwin's dataset and the predicted values
How to plot the residuals?The residual is calculated using:
Residual = Actual points - Predicted points
The actual points are:
(1,43), (3, 36), (5,22), (6, 25), (8,14)
The predicted points are:
(1,44), (3, 35), (5,26), (6, 22), (8,13)
Using the residual formula above, we have the residuals to be:
(x,y) = (1,-1), (3, 1), (5,-4), (6, 3), (8,1)
See attachment for the residual plot
Read more about residuals at:
https://brainly.com/question/1447173
Jasmine got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 23 cents per yard. If after that purchase there was 19.71 left on the card, how many yards of ribbon did jasmine buy?
Answers
Answer:
23 Yards
Step-by-step explanation:
So for this question, we would have to start off with writing an equation: 19.71+0.23x=25 once we subtract 19.71 on both sides, the left over sum of money will be 5.29. Since we are dealing with BOTH Dollars and Cents, it should be remembered to use 23 CENTS instead of Dollars. [tex]\frac{5.29}{0.23}[/tex]= 23 so the finals answer is 23 yards.
Answer:
23 Yards
Step-by-step explanation:
So for this question, we would have to start off with writing an equation: 19.71+0.23x=25 once we subtract 19.71 on both sides, the left over sum of money will be 5.29. Since we are dealing with BOTH Dollars and Cents, it should be remembered to use 23 CENTS instead of Dollars. = 23 so the finals answer is 23 yards.
Please help, I'm stuck
Suppose ten distinct, positive integers have a median of $10$. ("Distinct integers" means that no two integers are the same.)
What is the smallest the average of those ten integers could be?
Explain your answer in complete sentences.
Answers
Answer:
8 (or 8.4)
Step-by-step explanation:
First, the problem states the words: Distinct and positive.
That means that the smallest number we can use is 0.
We can make 10 blanks for 10 numbers for us to fill in.
_ _ _ _ _ _ _ _ _ _
Since 10 is an even number, and the median is not one single number, it will be the middle of the two numbers.
In this case, our two numbers are the 5th and 6th blank.
Any two numbers can be used, as long as they are the same actual value from 10.
Let us first put in the numbers we can, which are the numbers before the two middle blanks.
0,1,2,3, _ _ _ _ _ _
To find the median between two numbers, we can do:
(a+b) divided by 2 = median
We can use the smallest following number, 4. Then the 6th number will have to be 16 for 10 to be in the middle.
Also try the largest possible number for the 5th blank, 9. Then the 6th number will be 11.
4+16 and 9+11 both equal 20, and 20 divided by 2 is 10. So both of these work.
Now let's place the other numbers in for these two equations.
0,1,2,3,4,16,17,18,19,20
0,1,2,3,9,11,12,13,14,15
If we add the numbers of each together, we get:
0,1,2,3,4,16,17,18,19,20=100
0,1,2,3,9,11,12,13,14,15= 80
If we now divide each sum by 10 (to find the average) we get:
10
8
Since both of these were the most we could go, one with the 5th number as small as possible and one with the 5th number as large as possible.
Since the smaller answer we got was 8, the answer must be 8.
(I believe 0 is a positive integer because it doesn't carry a negative sign. If 0 is not a positive integer, the answer is 8.4. Use the same process
Omg please help! NO LINKS NO FILES PLEASE!
Answers
Answer: Square is a 17*17. Ok so its 121-25=96
Step-by-step explanation:
96
Solve the following equation for x to find the total number of people who downloaded songs from a music site for a certain month:
x = 0.6x + 384
How many people downloaded songs from the site that month?
Answers
Answer:
960 people.
Step-by-step explanation:
x = 0.6x + 384
x - 0.6x = 384
0.4x = 384
x = 384 / 0.4 = 960.
perform the translation (x, y) - (x-2, y+3)
Answers
Answer:
The coordinate of the image of a point is (2, +3) under the translation (x , y) → (x - 2),( y + 3). Find the coordinate of the preimage.
We are just looking for x and y and we know (2, +3) → (x - 2, y + 3)
2 = x - 2
x = 4
-3 = y + 3
y = -6
(x , y) = (4, -6)
How to find a
Hest answer = Brainilest
Archie is playing hide-and-seek with Valerie and Anya. Valerie is hiding 60 feet south of Archie and Anya is hiding due west of Valerie. If Archie is 100 feet from Anya, how far apart are Valerie and Anya?
Answers
Answer 116•6 feet
Hope it is helpful
Which statements accurately describe the triangles? Check all that apply.
The common ratio between the triangles is because
3 ** -3,
The common radio between the langles is 2.5 because -25,
The triangles could be similar
The triangles could not be similar
The ratio of the sidelengths are not consistent
The ratio of the side lengths are consistent
Answers
Answer:
the ratio of the side lengths are consistent
a yard is a shape of a triangle the height is 35 ft, and the width of 50 ft. what is the area.
Answers
Answer:
1,750
Step-by-step explanation:
35x50 that's the entire process
Two complementary angles have measures of ( 4x+5) and (2x+7) . What is the value of x?!
Answers
Answer:
(4x+5)=57 (2x+7)=33
Step-by-step explanation:
So, if a complementary angle is 90, our equation is (4x+5)+(2x+7)=90, and we get 13, so x=13, and we put that into our equation, so our first equation is now
Our first solution is (4(13)+5), which equals 57, and our second model is (2(13)+7), which equals 33, hence the angles' degrees are 57 and 33.
Point K is shown on the number line below .
Which number sentence BEST describes the value represented by point K?
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Answer: B. K < 13. K is 12.5, 12.5 is less than 13
1. Its not D because at the ending points of the number line; 10-20, which is less than 30.
2 It is not C because K is not on 15
3 It is not A because 12.5 is less than 13.
Hope it helps!!
$20,000 is borrowed at an interest rate of 15% p.a. (per annum) to be paid back over 10
years, calculate the amount of interest, the total repayment and the monthly repayment.
Answers
Answer:
30000 simple interest ,50000 total repayment.
Step-by-step explanation:
sorry iam terrible at explaining,
Find the indicate values
f(x)=2x-5
Answers
Find the common factor of all the terms of the polynomial 16x2 - 14x. O A. 2x² O B. 44² O c. 2x O D. 4x
Answers
Answer:
c. 2x.
Step-by-step explanation:
16x2 - 14x
Common factor of 16 and 14 = 2'
for x2 and x it is x,
Answer: 2x.
Can you help me with this
Answers
Answer:
Step-by-step explanation:
For the zeros, c is shows the correct number of zeros -- 7.
But you should note that the answer ought to contain the correct number of sig digs. There are 3. 692 The 2 cannot be dropped. Still your answer is correct.
Joey has 23 cards in his baseball card collection. Monica has 24 cards in her collection. How many times more cards does Monica have than Joe?
Answers
Answer:
Monica has 1 more card than Joey
Step-by-step explanation:
its simple math
What is the explicit formula for the sequence 8, 10, 12.5, 15.625, …?
Answers
So, an = 8(1.25)n - 1
Solve: 3x - 3= x +5
please can someone solve this I will give brainiest
Answers
3x - 3= x + 5
=> 3x - x = 5 + 3
=> 2x = 8
=> x = 8/2
=> x = 4
Answer:
4
Step-by-step explanation:
3x - 3 = x+5
=> 3x = x+5+3 ( transposing method)
=> 3x-x = 5+3
=> 2x = 8
=> x = 8/2
=> x = 4
What is the h concentration in a solution with a ph of 1.25? round to the nearest hundredth. × 10n m n=
Answers
The pH is the measure of hydrogen ion concentration in a solution. The hydrogen ion concentration at pH 1.25 is [tex]5\times 10^{-2}\ M[/tex].
How to calculate hydrogen concentration?The pH is the negative logarithmic value of the hydrogen ion concentration in the sample.
The pH can be expressed as:
[tex]\rm pH=-Log[H^+][/tex]
The hydrogen ion concentration can be given as:
[tex]\rm [H^+]=10^{-pH}[/tex]
The given pH is 1.25 The hydrogen ion concentration is given as:
[tex]H^+=10^{-1.25}\\H^+=0.05\ M\\h^+=5\times10^{-2}\ m[/tex]
The hydrogen ion concentration in the solution is .[tex]5\times 10^{-2}\ M[/tex]
Learn more about pH, here:
brainly.com/question/491373
Answer:
1st blank is 5.62
2nd blank is -2
Step-by-step explanation:
Look at the image (top right corner)