To find the inverse of a function, follow these steps: replace f(x) with y, interchange x and y, solve for y, and replace y with f-1(x). Applying these steps to the given function f(x) = 3x - 2 results in the inverse function f-1(x) = (x + 2)/3.
Explanation:To find the inverse of a function, we can follow these steps:
Replace the function notation f(x) with yInterchange x and y in the equationSolve the resulting equation for yReplace y with f-1(x)Let's apply these steps to the given function f(x) = 3x - 2:
Replace f(x) with y: y = 3x - 2Interchange x and y: x = 3y - 2Solve for y: x + 2 = 3yTherefore, the inverse of the function f(x) = 3x - 2 is f-1(x) = (x + 2)/3.
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The inverse function of [tex]\( f(x) = 3x - 2 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x + 2}{3} \).[/tex]
To find the inverse function [tex]\( f^{-1}(x) \)[/tex] for the given function [tex]\( f(x) = 3x - 2 \)[/tex], follow these steps:
Start with the original function:
[tex]\[ y = 3x - 2 \][/tex]
Swap y and x to find the inverse:
[tex]\[ x = 3y - 2 \][/tex]
Solve for y:
[tex]\[ x + 2 = 3y \][/tex]
[tex]\[ y = \frac{x + 2}{3} \][/tex]
Rewrite y as [tex]\( f^{-1}(x) \):[/tex]
[tex]\[ f^{-1}(x) = \frac{x + 2}{3} \][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[f^{-1}(x) = \frac{x + 2}{3}\][/tex]
Complete Question:
If [tex]f(x) =3x-2[/tex], find [tex]f^{-1}(x)[/tex]
In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red.
If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?
-1/8
-1/2
-2/3
-3/4
In the diagram, the radius of the outer circle is 5cm and the area of the shaded region is 16π cm^2. What is the radius or the inner circle?
By using the area of the ring we will see that the radius of the inner circle is 3cm.
What is the radius of the inner circle?
I assume that we have some kind of ring. To get the area of the ring, we need to take the area of the circle defined by the outer radius of the ring, and subtract the area defined by the circle with the inner radius of the ring.
Remember that the area of a circle of radius R is:
A = pi*R^2
We know that:
The radius of the outer circle is 5cm, so its area is:
A = pi*(5cm)^2 = pi*25cm^2
And the area of the ring is pi*16 cm^2
Then the area of the inner circle should be such that:
pi*25cm^2 - A' = pi*16cm^2
Then, solving for A'
A' = pi*25cm^2 - pi*16cm^2 = pi*9cm^2 = pi*(3cm)^2
So the radius of the inner circle is 3cm.
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A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?
Rewrite with only sin x and cos x.
sin 2x - cos 2x
Select one:
a. 2 sin2x - 2 sin x cos x + 1
b. 2 sin x
c. 2 sin2x + 2 sin x cos x - 1
Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. How much will Vivian pay for her surgery if it costs $9600?
2320
2420
2820
after doing the math and writing it out. it has to be one of these three answers but i do beleive that its the second answer but i need reassurance
We have been given that Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. We have been given that her surgery costs $9600 and we need to find how much will Vivian have to pay for her surgery.
Since we know that the insurance company will pay any amount after Vivian has paid $500. Therefore, the remaining amount after Vivian pays $500 as deductibles will be $9600 - $500 = $9100.
Now we know that Vivian's insurance company will pay 80% of this amount, therefore, Vivian will have to pay the 20% of $9100 in addition to the $500 she already paid.
20% of $9100 is [tex]9100\cdot \frac{20}{100} = \$1820[/tex]
Therefore, the total amount that Vivian pays for surgery is $500 + $1820 = $2320.
Therefore, the first choice given is the right answer.
A right triangle has sides if length 4,12 and 13 what is its perimeter
Answer:
29
Step-by-step explanation:
The perimeter is the sum of the side lengths:
4 + 12 + 13 = 29
The perimeter of the triangle is 29. (It is not a right triangle.)
___
A right triangle with side lengths 12 and 13 will have a short side of 5. Its perimeter is 30.
Find the sum of the series
When darcy's school bus travels at 30 miles per hour, it gets from her home to school in 12 minutes. what is the speed of darcy's bus if it makes the same trip in 18 minutes?
YO!!!!!!WILL GIVE 100 POINTS!!!!!!!!!!!BRAIN!!!!!!!!!!!!
Answer:
Following function:
f (x) = {(x + 2)²} × (x-4) × (x + 1)³
The roots are given by:
{(x + 2)²} × (x-4) × (x + 1)³ = 0
x + 2 = 0
x = -2
x-4 = 0
x = 4
x + 1 = 0
x = -1
Answer:
option A
Step-by-step explanation:
Factor the trinomial below.
9x2 + 6x + 1
A. (9x + 1)(x – 1)
B. (9x + 1)(x + 1)
C. (3x + 1)(3x + 1)
D. (3x + 1)(3x – 1)
True or False: A rectangular equation that is not a function may be a function in the polar coordinate system
The given statement is true.
The given statement is a rectangular equation that is not a function that may be a function in the polar coordinate system.
What is a rectangular equation?A rectangular equation or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane.
Polar equations indeed can describe graphs as functions, even when the equations in the rectangular coordinate system are not one of the functions. Polar equations can be graphed accurately using hands by using the Polar Coordinate System.
Therefore, the given statement is true.
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The population of a city has increased by 26 % since it was last measured. If the current population is 44,100 , what was the previous population?
The previous population of the city was 35000.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Assume the previous population to be [x].
Then, we can write -
x + 26% of x = 44100
x + 26x/100 = 44100
x + 13x/50 = 44100
(50x + 13x)/50 = 44100
63x = 44100 x 50
63x = 2205000
x = 35000
Therefore, the previous population of the city was 35000.
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The previous population of the city was 35,000 before experiencing a 26% increase to the current population of 44,100.
Explanation:To calculate the previous population of a city that has experienced a 26% increase to its current population of 44,100, we need to reverse the percentage increase. The formula for this is:
Previous population = Current population / (1 + Percentage increase)
In this case, the percentage increase is 26%, or 0.26 in decimal form. The calculation is:
Previous population = 44,100 / (1 + 0.26) = 44,100 / 1.26
This gives us:
Previous population = 35,000 (rounded to the nearest whole number)
Hence, the previous population of the city was approximately 35,000 before the 26% increase to the current 44,100.
Choose the best answer.
The most expensive type of life insurance is:
term insurance
whole-life insurance
endowment life insurance
limited-payment life insurance
Answer:
Endowment life insurance
Step-by-step explanation:
got it right on odyssey
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)^6 are _____.
Answer:
1, 6, 15, 20, 15, 6, 1
Step-by-step explanation:
The rectangular prism shown has a volume of 140 m3. This prism is enlarged using a scale factor of 2. What is the volume of the enlarged prism?
Help please !!!!!!!!!!!
Air is escaping from a spherical balloon at the rate of 4cc/min. how fast is the surface area of the balloon shrinking when the radius is 24 cm? (a sphere of radius r has volume 4 3 πr3 and surface area 4πr2 .)
-9 > -2 -3/4v solve.
Find the average value have of the function h on the given interval. h(u) = (15 − 10u)−1, [−1, 1]
The average value have of the function h(u) = (15 − 10u)−1 on the given interval [−1, 1] is -5.
What is average value of the function?The average value of a function is given by the formula:
[tex]fav = \frac{1}{b - a} \int\limits^b_a f({x}) \, dx[/tex]
Now the given function is,
h(u) = (15 − 10u) − 1
or, h(u) = 15 − 10u − 1
or, h(u) = 14 − 10u
So, the average value on the given interval [−1, 1] is given as:
[tex]fav = \frac{1}{1 - (-1)} \int\limits^1_{-1} h({u}) \, du[/tex]
Thus, putting the value of h(u) we get,
[tex]fav = \frac{1}{(1 + 1)} \int\limits^1_{-1} (14 - 10u) \, du[/tex]
Thus integrating we get,
fav = (1/2) { [14u] - [10u²/2]
⇒ fav = (1/2) { [14u] - [5u²]
Applying the limits we get, -1 to 1,
⇒ fav = (1/2) { 14[-1 + 1] - [5{-1² + 1²}]
Solving we get,
⇒ fav = (1/2) { 14[0] - [5{1 + 1}]
⇒ fav = (1/2) {- [5{2}]
⇒ fav = -5
Thus, the average value have of the function h(u) = (15 − 10u)−1 on the given interval [−1, 1] is -5.
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What is the perimeter of rectangle that is 92 feet long and 46 feet wide?
The perimeter of a rectangle that is 92 feet long and 46 feet wide is calculated using the formula P = 2l + 2w, resulting in a perimeter of 276 feet.
Explanation:The question asks for the perimeter of a rectangle with specific dimensions. To calculate the perimeter of a rectangle, we use the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. Given that the rectangle is 92 feet long and 46 feet wide, we substitute these values into the formula to get the perimeter: P = 2(92) + 2(46) = 184 + 92 = 276 feet.
Therefore, the perimeter of the rectangle is 276 feet.
Write the quadratic function in vertex form: f(x) = 4x2 + 2x -5
A)f(x) = 4(x + 14)2 - 214B)f(x) = 4(x + 116)2 - 214C)f(x) = 4(x + 14)2 - 194D)f(x) = 4(x + 116)2 - 194
Answer:its B
Step-by-step explanation:
f(x) = -4 (x + 1/4)² - 15/4
exactly 2/5 of the unversity students live off campus. Of those students, 3/10 of them live at home. what fraction of the univesity's students live at home? Reduce your answer to lowest terms
Compare your prediction with the total number of pennies on Row 1. How would you change your estimate? Is the result surprising?
Answer:
a statement that your prediction was less than or greater than the actual count
a statement about how you would change your estimation process
Step-by-step explanation:
Choose any of these two.. There both correct btw
The statements that is true about your prediction of the total pennies on rows 1-4 are statement (b) and (d).
A predictive function is one of mathematical function that helps us to know about future events based on past events. There are many types of functions that can be classified as predictive functions.
The prediction was off by greater than 1,000,000 of the actual total. After seeing the result for rows 1-4, you would indeed change your prediction for the total because it indicates a significant deviation.
Complete question
Check every statement that is true about your prediction of the total pennies on rows 1-4.
a) Your prediction was off by less than or equal to 1,000,000 of the actual total.
b) Your prediction was off by greater than 1,000,000 of the actual total.
c) After seeing the result for rows 1-4, you would change your prediction for the total.
d After seeing the results for rows 1-4, you would not change your prediction for the total.
Last Monday, Luis's mother gave birth to twins and named them Ashley and Umaima. When they were first born, Ashley weighed 2.82.8 2.8 2, point, 8 kilograms , and Umaima weighed 2.52.5 2.5 2, point, 5 kilograms and was 4949 49 49 centimeters tall. How much did the babies weigh in total?
which of the following parametric equations are equivalent to the polar equation r=3 cos theta
Answer:
B
Step-by-step explanation:
A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 miles above sea level. The radius of the Earth is 3959 miles. What is the climber's distance to the horizon?
Geo: Topic 3- Parallelograms 1pt A rhombus is a parallelogram with all four sides of equal length. One way to determine if a given parallelogram is a rhombus is to test whether its diagonals are perpendicular. The vertices of a parallelogram are M(−1,2), N(9,2), P(3,−6), and Q(−7,−6). Determine whether the parallelogram is a rhombus by checking to see if the diagonals are perpendicular. What is the slope of MP¯¯¯¯¯¯? What is the slope of NQ¯¯¯¯¯¯? Are diagonals MP¯¯¯¯¯¯ and NQ¯¯¯¯¯¯ perpendicular? Is the parallelogram a rhombus?
A color called “shocking pink” is made by mixing red paint with white paint. The ratio of red to white is 2 to 7. How much red paint should be mixed with 16 fl. oz of white paint?
Answer:
4.5 oz
Step-by-step explanation:
solve the equation 4(-x+4)=12
The shortest side of a right triangle measures 88 m. the lengths of the other two sides are consecutive odd integersodd integers. find the lengths of the other two sides.