Find the inverse of the function below and sketch by hand a graph of both the function and its inverse on the same coordinate plane.
Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded.
f(x)=x^2+2 with the domain x \geq0
Answers
The inverse function is:
f⁻¹(y) = √(y - 2), where y ≥ 2.
What is an inverse function?An inverse function is a function that "undoes" the action of another function. In other words, if we start with a value, apply a function to it, and then apply the inverse function to the result, we should get back to the original value. For example, if we have a function f(x) that doubles a number, the inverse function would be one that halves a number. The notation for an inverse function is f⁻¹(x), and it is defined as follows:
If f is a function with domain A and range B, then its inverse function f⁻¹ is a function with domain B and range A, where f⁻¹(y) = x if and only if f(x) = y.
According to the given informationTo find the inverse of the function f(x) = x² + 2, we need to solve for x in terms of y.
Step 1: Replace f(x) with y.
y = x² + 2
Step 2: Solve for x in terms of y.
y - 2 = x²
±√(y - 2) = x
Note that we use ± because when we take the square root of a number, we get both a positive and a negative solution. However, since the domain of the function is x ≥ 0, we only consider the positive solution.
So the inverse function is:
f⁻¹(y) = √(y - 2), where y ≥ 2.
To sketch the graphs of f(x) and f¹(x) on the same coordinate plane:
Step 1: Plot a few points on the graph of f(x).
We can choose some x-values, plug them into f(x) to find the corresponding y-values, and then plot the points (x, y) on the coordinate plane. For example:
f(0) = 2, so (0, 2) is a point on the graph.
f(1) = 3, so (1, 3) is a point on the graph.
f(2) = 6, so (2, 6) is a point on the graph.
We can also notice that the graph is a parabola that opens upward and has its vertex at (0, 2).
Step 2: Reflect the points across the line y = x to get the graph of the inverse function.
To do this, we swap the x and y coordinates of each point on the graph of f(x) to get the corresponding point on the graph of f⁻¹(x). For example:
(0, 2) becomes (2, 0)
(1, 3) becomes (3, 1)
(2, 6) becomes (6, 2)
We can also notice that the graph of f⁻¹(x) is a curve that starts at (2, 0) and moves upward as x increases.
Step 3: Plot the graphs of both functions on the same coordinate plane.
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Related Questions
Based on this equation, estimate the rating of chips whose cost is $1.10.
Round your answer to the nearest hundredth.
Answers
The estimated rating of chips whose cost is $1.10 is 2.25.
Estimating the rating of chips whose cost is $1.10.From the question, we have the following parameters that can be used in our computation:
y = 2.5x - 0.5
To estimate the rating of chips whose cost is $1.10, we can substitute x = 1.10 into the equation y = 2.5x - 0.5 and solve for y.
y = 2.5x - 0.5
y = 2.5(1.10) - 0.5
y = 2.75 - 0.5
y = 2.25
Therefore, the estimated rating of chips whose cost is $1.10 is 2.25. Rounded to the nearest hundredth, it is 2.25.
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Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d= 163t
D. d= 81.50t
Answers
Answer:
C. d= 163t represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours. This is because Rajindri earns $163 for every two hours that she works, which means she earns $81.50 for each hour that she works. Therefore, the equation that relates the number of dollars earned to the number of hours worked is d = 163t.
Step-by-step explanation:
Pleaseeeee helppp meeee
Answers
Subtracting 8 times the first row to the second row we will get the matrix.
[tex]\left[\begin{array}{ccc}1&10&-23\\0&-83&249\end{array}\right][/tex]
How to get a zero in row 2, column 1?To get that, you will need to take row 2 and subtract 8 times row 1, then the values of each column will be:
Remember that the rows are the horizontal vectors and the columns are the vertical ones.
8 - 8*1 = 0
-3 - 8*10 = -83
65 - 8*-23 = 249
Then the new matrix will be:
[tex]\left[\begin{array}{ccc}1&10&-23\\0&-83&249\end{array}\right][/tex]
That is the matrix with a zero in row 2, column 1.
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what is an equation of the image of the line after dilation
Answers
An equation of the image of the line after dilation is -30x - 20y = -8.
What is scale factor?In Mathematics and Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.
Generally speaking, the transformation rule for the dilation of a geometric object based on a specific scale factor of 5 is given by this mathematical expression:
(x, y) → (kx, ky)
Where:
x and y represents the data points.k represents the scale factor.Therefore, the transformation rule for this dilation is given by;
(x, y) → (kx, ky)
(x, y) → (5(-6x), 5(-4y)) = -30x - 20y = -8.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Calculate how far up the wall the ladder reaches
Answers
The maximum height of the ladder on the wall is given as follows:
h = 8.7 m.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the angle of 60º, the parameters are given as follows:
Adjacent side: 5 m.Opposite side: maximum height.Hence the maximum height is obtained as follows:
tan(60º) = h/5
h = 5 x tangent of 60 degrees
h = 8.7 m.
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answer and explain in detail
Answers
Answer:
The area of right-angled triangle is 30 cm².
Step-by-step explanation:
Given : Here we given that the base and hypotenuse of triangle 12 cm and 13 cm respectively.To Find : We have to find the area of right-angled triangle but before we will find the height of the triangle.Solution :By using Pythagoras Theorem we will find the hypotenuse of triangle :
[tex] \sf{\longrightarrow{{(Hypotenuse)}^{2} = {(Height)}^{2} + {(Base)}^{2}}}[/tex]
Substituting all the given values in the formula to find hypotenuse :
Hypotenuse = 13 cmBase = 12 cm[tex]\sf{\longrightarrow{{(Hypotenuse)}^{2} = {(Height)}^{2} + {(Base)}^{2}}}[/tex]
[tex]\sf{\longrightarrow{{(13)}^{2} = {(Height)}^{2} + {(12)}^{2}}}[/tex]
[tex]\sf{\longrightarrow{(13 \times 13) = {(Height)}^{2} + {(12 \times 12)}}}[/tex]
[tex]\sf{\longrightarrow{(169) = {(Height)}^{2} + {(144)}}}[/tex]
[tex]\sf{\longrightarrow{{(Height)}^{2} = 169 - 144}}[/tex]
[tex]\sf{\longrightarrow{{(Height)}^{2} = 25}}[/tex]
[tex]\sf{\longrightarrow{{(Height)} = \sqrt{25}}}[/tex]
[tex]\sf{\longrightarrow{\underline{\underline{\red{(Height) = 5 \: cm}}}}}[/tex]
Hence, the height of triangle is 5 cm.
[tex]\begin{gathered} \end{gathered}[/tex]
Now, calculating the area of right-angled triangle by substituting all the given values in the formula :
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2}bh}}[/tex]
b (Base) = 12 cmh (Height) = 5 cm[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2}bh}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2} \times b \times h}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2} \times 12\times 5}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = 6\times 5}}[/tex]
[tex]\dashrightarrow{\sf{\underline{\underline{\pink{Area_{(\triangle)} =30 \: {cm}^{2}}}}}}[/tex]
Hence, the area of triangle is 30 cm².
—————————————————Which of the following is true for the traditional economy?
Answers
Answer:
They barter, or trade (without using money). Economic systems are based on customs, traditions, and beliefs of the past.
Step-by-step explanation: -
URGENT!! Please help
Answers
The correlation coefficient between the minutes the actor appeared shirtless in a film and the film's opening weekend gross is 0.75.
How to write the linear regression equation and determine the correlation coefficient?In this scenario, the minutes shirtless (x) would be plotted on the x-axis of the scatter plot while the open weekend gross (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the minutes shirtless (x) and the open weekend gross (y), an equation for the linear regression is given by:
y = 10.83 + 0.86x
Correlation coefficient, r = 0.7488571925 ≈ 0.75
In conclusion, we can logically deduce that there is a strong correlation between the data because the correlation coefficient (r) is approximately greater than 0.7;
0.7＜|r| ≤ 1 (strong correlation)
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A wave is traveling at a speed of 3.4m/s has a length of 1.3m. what is its frequency?
Answers
The frequency of the wave is 2.62 Hz
Find the measure of
Answers
The measure of ∠LPN is 57°.
What is arc?An arc is a segment of a circle in geometry that is typically defined by two endpoints and the arc itself, which is the collection of all points on the circle that are situated between the two endpoints.
The subtendency of an arc can be measured by measuring its central angle.
Since angles inscribed in the same arc are congruent, we have:
m(arc LP) = m(arc NP) = 102° + 144° = 246°
Now, using the fact that the sum of the measures of the arcs of a circle is 360°, we have:
m(arc LM) + m(arc LP) + m(arc NP) + m(arc MN) = 360°
Substituting the known values, we get:
m(arc LM) + 246° + m(arc MN) = 360°
Simplifying, we have:
m(arc LM) + m(arc MN) = 114°
But angles inscribed in the same arc are congruent, so we have:
m(∠LPN) = (m(arc LM) + m(arc MN))/2
Substituting the value we found for m(arc LM) + m(arc MN), we get:
m(∠LPN) = 114°/2 = 57°
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nangle
In order to justify your general statement above (to give a reason why it is true), construct the angles A, B
and C of triangle 1 around point M as in the diagram below.
H
Are [MN] and [ML] on the same straight line?
Answers
Answer:
MN and ML are on the same straight line.
At a local college 29 of the male students are smokers and 262 are non smokers. Of the female students, 40 are smokers and 360 are non smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers
Answers
The probability that both a male student and a female student from the college are smokers is 0.01 or 1%.
We have,
Let's first find the probability of selecting a male smoker and then the probability of selecting a female smoker.
P(Male smoker) = Number of male smokers / Total number of male students
P(Male smoker) = 29 / (29 + 262)
P(Male smoker) = 0.10
Similarly, the probability of selecting a female smoker is:
P(Female smoker) = Number of female smokers / Total number of female students
P(Female smoker) = 40 / (40 + 360)
P(Female smoker) = 0.10
Now, we can find the probability of selecting both a male smoker and a female smoker by multiplying the probabilities:
P(Both smokers) = P(Male smoker) x P(Female smoker)
P(Both smokers) = 0.10 x 0.10
P(Both smokers) = 0.01
Therefore,
The probability that both a male student and a female student from the college are smokers is 0.01 or 1%.
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The price of an item has been reduced by 25%. The original price was $35
Answers
Step by step
Original price $35
Less (reduced) by 25%
Let x = sale price
X = 35 - (35 * .25)
X = 35 - 8.75 = $26.25 sale price
the expression 30 x squared - 100x - 60 and (5x-20) (6x+3) define the same function f. Which expression makes it easier to find f of 0
Answers
question-amp-image
Explaining
Solve the system of equations.
y = 2 - 6x
1/2y - x = 1
Question 4 options:
(0,-2)
(2,0)
(-2,0)
(0,0)
(1,-4)
Answers
Answer:
Step-by-step explanation:
We can start by solving the second equation for y:
1/2y - x = 1
1/2y = x + 1
y = 2x + 2
Now we can substitute this expression for y into the first equation:
y = 2 - 6x
2x + 2 = 2 - 6x
Adding 6x to both sides, we get:
8x + 2 = 2
Subtracting 2 from both sides, we get:
8x = -0
Dividing both sides by 8, we get:
x = 0
Now we can use this value of x to find y:
y = 2x + 2
y = 2(0) + 2
y = 2
Therefore, the solution to the system of equations is x=0 and y=2.
reduce to lowest terms 4x^y^3/-8x^2y
Answers
Answer:
x^(y^3-1) / -2xy
Step-by-step explanation:
4x^y^3 = 4x^(y^3)
-8x^2y = -8x^2y^1
= 4x^(y^3) / -8x^2y^1
= (4x^(y^3) / 4xy) / (-8x^2y^1 / 4xy)
= x^(y^3-1) / -2xy
Answer:
Step-by-step explanation:
I’m stuckkkk please helpppp
Answers
The hiking trial at the state park that is the longest would be D. Hilltop
How to find the longest hiking trail?To find the hiking trail that is longest, convert the lengths shown to one form so as to see which is the longest.
Mammoth = 8.005 kilometers
Brookside = 8. 7 kilometers
Wild Rose = 8, 080 meters = 8. 08 kilometers
Hilltop = 8 kilometers 800 meters = 8. 8 kilometers
This then shows that the hiking trail that is the longest in the state park is the Hilltop trail which goes for 8. 8 kilometers.
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Help is my work right?
Answers
Answer:
32[tex]a^{35}[/tex]
Step-by-step explanation:
using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex](2a^3a^4)^{5}[/tex]
= (2[tex]a^{(3+4)}[/tex] )^5
= [tex](2a^7)^{5}[/tex]
raise each term inside the parenthesis to power 5
= [tex]2^{5}[/tex] × [tex]a^{7(5)}[/tex]
= 32[tex]a^{35}[/tex]
Answer:
32[tex]a^{35}[/tex]
Step-by-step explanation:
using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex](2a^3a^4)^{5}[/tex]
= (2[tex]a^{(3+4)}[/tex] )^5
= [tex](2a^7)^{5}[/tex]
raise each term inside the parenthesis to power 5
= [tex]2^{5}[/tex] × [tex]a^{7(5)}[/tex]
= 32[tex]a^{35}[/tex]
Supplementary angles
Answers
The angle that is supplementary to the angle DEA is angle DEC
Finding the angle that is supplementary to the angle DEAFrom the question, we have the following parameters that can be used in our computation:
The lines HF and CAThe transversal line GEAlso from the question, we have
Angle = DEA
As a general rule;
Two angles are said to be supplementary if their sum add up tp 180 degrees
This means that the angles are on a straight line
The angle are on the same straight line with ange DEA is DEC
Hence, the angle is angle DEC
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Find the volume of the prism. Round your answer to the nearest tenth, if necessary.
cm³
18 cm
8 cm
16 cm
Answers
Answer: 2304.0 cm³
Step-by-step explanation: V = length x width x height
V = 18 cm x 8 cm x 16 cm
V = 2304 cm³
The winner of a contest will be blindfolded and then allowed to reach into a hat containing 29 $1 bills and 7 $100 bills. The winner can remove 4 bills from the hat and keep the money. Find the probability that the winner will pull out at least 1 $100 bill. (See Example 5 in this section. Round your answer to the nearest tenth of a percent.)
Answers
The probability that the winner will pull out at least one $100 bill is 7/36, or 19.4%.
What is probability?The probability of an event occurring is determined by the number of favorable outcomes divided by the total number of possible outcomes.
In this problem, the favorable outcome is that the winner will pull out at least one $100 bill, while the total number of possible outcomes is the number of ways to select 4 bills from the hat, which is 36.
Thus, the probability of the winner pulling out at least one $100 bill is calculated by dividing the favorable outcome by the total number of possible outcomes.
Since there are 7 $100 bills in the hat, the favorable outcome is 7. The total number of possible outcomes is 36, which is calculated by using the formula nCr, where n is the total number of objects and r is the number of objects selected.
In this case, n = 36 and r = 4, so the equation is 36C4.
Thus, the probability that the winner will pull out at least one $100 bill is 7/36, or 19.4%.
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The size P of a certain insect population at time t (in days) obeys the function P = 700e0.03t, After how many days will the population reach 1500?
Answers
the population will reach 1500 after about 30.1 days.
After how many days will the population reach 1500?We can solve for the time t by setting P = 1500 and solving for t:
1500 = 700[tex]e^{(0.03t)}[/tex]
Divide both sides by 700:
2.14 = [tex]e^{(0.03t)}[/tex]
Take the natural logarithm of both sides:
ln(2.14) = ln([tex]e^{(0.03t)}[/tex])
Using the logarithm property that ln([tex]e^{x}[/tex]) = x, we can simplify to:
ln(2.14) = 0.03t
Divide both sides by 0.03:
t = ln(2.14)/0.03
Using a calculator, we get:
t ≈ 30.1 days
Therefore, the population will reach 1500 after about 30.1 days.
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the temperature at noon was 10degree Celsius above 0 . if it decreases at the rate 2 degree Celsius per hour till midnight , at time the temperature would be 8 degree Celsius below zero ? what would be the temperature at mid-night?
Answers
Answer:
Time at which temperature will be -8 degrees Celsius = 21 00 (24 hour clock) or 9pm (12 hour clock)
Temperature at midnight = - 14°C
Step-by-step explanation:
The pic
Correct
The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. All measures are recorded in thousands of
dollars. The summary output for the regression model is given below.
df
SS
Regression 1 16.54127801
Residual 6 5.641280047
Total 7
22.18255806
ANOVA
MS
F
16.54127801 17.59311136
0.94021334
Significance F
0.005721150
Step 1 of 3: What is the coefficient of determination for this model, R2? Round your answer to four decimal places.
Answers
Answer:
17.023413
Step-by-step explanation:17.023413
Need help will give brainliest and 5 stars!
Looking for x and y intercepts, the hole and vertical asymptote.
Answers
Check the picture below.
It takes Sam 40 minutes to jog 5 kilometers. How far can he jog in 60 minutes?
Answers
Answer:
7.5 kilometers
Step-by-step explanation:
[tex]\frac{40}{5}[/tex] = [tex]\frac{60}{x}[/tex]
[tex]\frac{40}{5}[/tex] can be simplified to 8
8 = [tex]\frac{60}{x}[/tex] Multiply both sides by x
8x = 60 Divide both sides by 8
[tex]\frac{8x}{8}[/tex] = [tex]\frac{60}{8}[/tex]
x = 7.5
Helping in the name of Jesus.
The following describes a classroom environment for doing mathematics ". Which one does not fit
Answers
Group work and group discussion are discouraged is a factor that does not fit into the environment for doing mathematics
How is the environment for doing mathematicsThe mathematics scope can differ contingent upon a person's exact circumstances in addition to their individual preferences. As a whole, however, math is customarily studied and exercised within tranquil and absorbed settings that allow for intensive thought processes. A few typical conundrums for executing mathematics tasks encompass:
Libraries: Many mathematicians affectionately flock to libraries for their serene environment furthermore the availability of learning materials and related informational sources. University-focused facilities usually brag extensive selections of mathematics books as well as magazines.
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How many pounds of almonds priced $5.35 per pound should be mixed with peanuts worth $3.75 per pound in order to obtain 20 pounds of mixture that will sell for $4.50 per pound?
Answers
Answer:
9.375 pounds of almonds with 10.625 pounds of peanuts----------------------
To solve this problem, we can use a system of equations with two variables:
x = pounds of almonds at $5.35,y = pounds of peanuts at $3.75.
We have two equations based on the given information:
Solve the first equation for x:
x = 20 - ySubstitute the expression for x into the second equation:
5.35(20 - y) + 3.75y = 90Simplify and solve for y:
107 - 5.35y + 3.75y = 90-1.60y = -17y = 10.625Substitute the value of y back into the expression for x:
x = 20 - 10.625x = 9.375So, you should mix 9.375 pounds of almonds with 10.625 pounds of peanuts to obtain 20 pounds of mixture that will sell for $4.50 per pound.
Answer:
Step-by-step explanation:
You should mix 9.375 pounds of almonds with 10.625 pounds of peanuts to obtain 20 pounds of mixture that will sell for $4.50 per pound.
In settings where we can assume that each possible outcome is equally likely to occur we are
using theoretical probabilities. We do this when we expect a coin to have the same chance of
landing on heads as it does on tails. We also do this when we assume that if we roll a six sided
die each possible number has the same chance of landing up.
Answers
The statement on theoretical probabilities is True.
What is theoretical probability ?Theoretical probabilities, referred to as classical probabilities, are utilized when we can suppose that each conceivable result has an equal chance of happening.
Typically, this is observed in games of luck like tossing a coin or rolling dice, where the chances of every possible outcome are equivalent. Such scenarios permit one to use probability principles and determine the probability of each outcome transpiring.
For instance, with fair coins, it's reasonable to assert that there's an even likelihood for heads or tails, setting both probabilities at 1/2.
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25.
What is the height of a box if the width is x + 1, the length is x + 3, and the volume is x3 + 6x2 + 11x + 6? (Hint: Recall
that V= (wh.)
Ox+2
none of the answer choices
O-x-2
O x-2
-x+2
0
Answers
The height of box for the given cuboid satisfied the relation through which the volume of cuboid is satisfied is, height = x+2
What about volume of cuboid?
A cuboid is a three-dimensional shape that has six rectangular faces, where each face has four sides and four right angles. The volume of a cuboid is the amount of space that it occupies in three-dimensional space. It is measured in cubic units.
The formula to calculate the volume of a cuboid is given by multiplying its length, width, and height.
Volume of cuboid = Length x Width x Height
The volume of a cuboid can be used to determine the amount of space that it can hold or the amount of material required to fill it.
The volume of a cuboid can be calculated by multiplying its length, width, and height.
If the length of the cuboid is represented by "l", the width by "w", and the height by "h", then the volume can be calculated using the formula:
Volume of cuboid = l x w x h
According to the given information:
As, we know that the volume of cuboid = length x breath x height
Given volume of cuboid is = [tex]x^{3} + 6x^{2} +11x^{} + 6[/tex]
And width = x + 1 and length = x + 3.
Volume of cuboid = length x breath x height
⇒ [tex]x^{3} + 6x^{2} +11x^{} + 6[/tex] = (x + 1)(x + 3) x height
⇒ height = [tex]\frac{x^{3} + 6x^{2} +11x^{} + 6}{(x+1)(x+3)}[/tex]
⇒ height = [tex]\frac{(x+1)(x+2)(x+3)}{(x+1)(x+3)}[/tex]
⇒ height = (x+2)
So, the height of the given cuboid is (x+2)
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