Answers
9514 1404 393
Answer:
f^-1(x) = <see attachment>
Step-by-step explanation:
If we write the function as ...
f(x) = ∛x +101/128x
Then the inverse function is the value of y when ...
x = f(y)
This resolves to a cubic in y, whose solution can be found by use of any of the various cubic solution formulas. You can find the cubic by ...
x = ∛y +by . . . . . . where b = 101/128
x -by = ∛y . . . . . . . subtract by
(x -by)³= y . . . . . . cube both sides
If we subtract the left side and expand the cube, we get ...
b³y³ -3b²xy² +(1 +3bx²)y -x³ = 0 . . . . . . . a cubic in y
There will be one real and two complex solutions to this cubic. The real solution can be written in the form shown in the attachment. That is, ...
y = f⁻¹(x) = [attachment expression]
A graph of it is shown in the second attachment. It is the reflection of f(x) across the line y = x, as an inverse function should be.
_____
Additional comment
The idea here is to show that it is possible to write an expression for the inverse function. It is not pretty, and it is somewhat tedious to evaluate.
Related Questions
Let f(x) = x - 2, g(x) = -7x + 10, . Evaluate
f(g(1))
Help me pleazz
Answers
Answer:
[tex]f(x) = x - 2 \\ g(x) = - 7x + 10 \\ f(g(x)) = ( - 7x + 10) - 2 \\ f(g(x)) = - 7x + 10 - 2 \\ f(g(x)) = - 7x + 8 \\ f(g(1)) = - 7(1) + 8 \\ f(g(1)) = - 7 + 8 \\ \boxed{f(g(1)) = 1}[/tex]
f(g(1)) = 1 is the right answer.what is a rapid loan?
Answers
Answer:Rapid Loans Fast is the premier provider of cash advances, emergency and weekend loans. ... Thanks to the introduction of modern IT, the application for an online loan will take you no more than 5-10 minutes. Approval occurs automatically, after which the payday loans are instantly transferred to the borrower's bank card.
Step-by-step explanation:
What is the quotient of 3/4 and 5/6
Answers
Answer:
9/10 in fraction form 0.9 in decimal form
Step-by-step explanation:
Answer:
9/10
Step-by-step explanation:
keep change change, then multiply.
Find any solutions of x/x-1 + 2/x+2= -6/x^2+x-2
Answers
Answer:
a I think ooookkkkk
The solution of the equation x/(x-1) + 2/(x+2) = -6/(x²+x-2) represented by statement is option D. The equation has one true solution and one extraneous solution.
To find the solutions to the equation, we need to simplify and solve for x:
x/(x-1) + 2/(x+2) = -6/(x²+x-2)
Factor the denominators on both sides of the equation.
The denominator on the left side can be factored as follows:
x² + x - 2 = (x+2)(x-1)
Find the common denominator.
The common denominator for the left side is (x-1)(x+2).
Rewrite the fractions with the common denominator:
[(x+2) × x]/[(x-1)(x+2)] + [2 × (x-1)]/[(x-1)(x+2)] = -6/[(x+2)(x-1)]
Combine the fractions,
[x(x+2) + 2(x-1)] / [(x-1)(x+2)] = -6/[(x+2)(x-1)]
Eliminate the denominator:
Multiply both sides by (x+2)(x-1) to eliminate the denominators:
[x(x+2) + 2(x-1)] = -6
Expand and simplify the equation:
x² + 2x + 2x - 2 = -6
x² + 4x - 2 = -6
x² + 4x + 4 = 0
Solve for x using the quadratic formula:
x = (-b ± √(b²-4ac)) / 2a
Here, a = 1, b = 4, and c = 4.
x = (-4 ± √(4² - 4 × 1 × 4)) / 2× 1
x = (-4 ± √(16 - 16)) / 2
x = (-4 ± √0) / 2
x = (-4 ± 0) / 2
x = -4 / 2
x = -2
The equation has one true solution, x = -2 (repeated root).
Now, let's check this solution in the original equation:
x/(x-1) + 2/(x+2) = -6/(x²+x-2)
(-2)/((-2)-1) + 2/((-2)+2) = -6/((-2)²+(-2)-2)
(-2)/(-3) + 2/0 = -6/(4-2-2)
2/0 is undefined, and since we cannot divide by zero, we have an extraneous solution.
Therefore, the correct statement for the solution is option D. The equation has one true solution and one extraneous solution.
learn more about solution here
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P is the set of integers that are greater than or equal to -3 and less than -1
Answers
Which fraction is equivalent to the one shown below?
Answers
Subtracting a negative becomes addition.
Both of the subtractions are subtracting a negative , so they both become addition.
Answer: D. 18 5/8 + 22 2/5 + 40 1/5
what is the like term for 4x^2
Answers
Answer:
Step-by-step explanation:
4x^2+5x^2+x^2
what is f(-1) for the graph shown below?
Please help
Answers
Answer:
f(-1)= -3
Step-by-step explanation:
We all know f(x) = y
Since x= -1, y= -3 as per given in the graph, so
f(-1)=-3
which transformation would result in a geometric figure
Answers
Answer:
You reflect it, Translated and Rotate it
Step-by-step explanation:
hope this helps
pls help!!!!!!!!!!!!!!
Answers
Answer:
HMmMm I think the answer is yes
How long should an escalator be if it is to make an angle 30 with the floor and
Answers
Answer:
it should be 23 feet long
Step-by-step explanation:
HELP ME WORTH 10
A. The number of gallons in the tank after one hour
B. The rate of change of gas in her tank over time
C. The number of gallons of gas at time x=0
D. How long it takes Ai Mi to run out of gas
Answers
Answer:
B
Step-by-step explanation:
the amount of gas in tank changes over time (hours)
pls correct me if I'm wrong hope this helps
help please i will give brainliest
Answers
Answer:
Give me branilest first you scammer
Step-by-step explanation:
Taci is studying a map before her hiking trip. on her map, 2 inches equals 85 miles. how far apart are two locations if they are 1.5 inches apart on the map? a. 63.75 miles c. 68 miles b. 113.33 miles d. 67.11 miles
Answers
Answer:
a
63.75
I decided 85 by 2 to get what one Ince would be and then multiplied that number by 1.5
Use the point and the slope to graph each line. Write the equation of the line.
The line passes through point (4,0) and has slope 0.5.
Answers
Answer:
slope = 0.5=1/2
using the formula y-y1 = m (x -x1)
y - 0 =1/2(x - 4)
y = 1/2 (x -4); cross multiply
2y = x -4
divide both sides by 2
y = 1/2x -2
y = 0.5x -2(equation of the line)
Write an equation (any form) for the quadratic graphed below:
Answers
Vertex is (2,3), so that gives us:
y=a(x-2)^2+3
Now the graph goes through (0,1), so plug that in to find a:
1 = a(0-2)^2+3
-2 = a(-2)^2
-2 = a•4
-1/2 = a
So, y = -1/2 (x-2)^2 + 3
Answer:
y = - ½(x - 2)² + 3
Step-by-step explanation:
Given the vetex, (2, 3), as the maximum point on the graph, along with the y-intercept, (0, 1):
We can substitute these values into the given vertex form of the quadratic equation:
y = a(x - h)² + k
where:
a = determines whether the graph opens up or down, and makes the parent function wider or narrower. If a is positive, the graph opens up; if a is negative, the graph opens down. If 0 < a < 1, the graph is wider than the parent function. If a > 1, the graph is narrower than the parent function.(h, k ) = vertexh = determines how far left or right the parent function is translated.k = determines how far up or down the parent function is translated.Use vertex = (2, 3) and y-intercept (0, 1) to solve for "a":
y = a(x - h)² + k
1 = a(0 - 2)² + 3
1 = a(-2)² + 3
1 = a(4) + 3
Subtract 3 from both sides:
1 - 3 = a(4) + 3 - 3
-2 = 4a
Divide both sides by 4 to solve for a:
-2/4 = 4a/4
- ½ = a
Therefore, the value of a = - ½. This means that the graph opens downward, and that the parabola is wider than the parent function.
The quadratic equation in vertex form given a = - ½, and vertex (2, 3) is:
y = - ½(x - 2)² + 3
Please mark my answers as the Brainliest if you find this explanation helpful :)
Find the mode(s) for the following group of data items.
33, 30, 29, 28, 34, 31, 27, 29
Select the correct choice below and, if necessary, fill in the answer box within your choice.
O A. The mode(s) is/are
(Use a comma to separate answers as needed.)
O. B. There is no mode.
Answers
2(2x - 3) > 6 solve for x
Answers
2(-3)=-6
4(6)=24
24-6=30
Answer:
x > 3
Step-by-step explanation:
2(2x -3) >6
4x - 6 > 6( collect the like terms)
4x > 12(divide both sides by 4)
x > 3
PLS MARK BRAINLIEST
Please answer correctly! Give the correct solution to get the right answer on the graph. Will give brainliest to the correct answer.
This is Algebra 2.
Answers
Using pemdas, please help with the following questions:
Answers
Answer:
Step-by-step explanation:
(9 + 33 - 6) ÷ 6 - 3²
36 ÷ 6 - 3² p
36 ÷ 6 - 9 e
6 - 9 md
- 3 as
(10 + 43 - 5) ÷ 6 + 5²
48 ÷ 6 + 5² p
48 ÷ 6 + 25 e
8 + 25 md
33 as
(6 + 3)² + (9 - 10 + 5)
9² + 4 p
81 + 4 e
81 + 4 md not used
85 as
4 x (12 x 6 - 4²) + 9 must use pemdas inside the parentheses first
4 x (12 x 6 - 16) + 9 e (p not used inside)
4 x (72 - 16) + 9 md
4 x 56 + 9 as parentheses complete, start over
224 + 9 md (pe not used)
233 as
someone help please!
Answers
a reduced fat cookie contains 11g of fat per serving. in order for food to be termed 'reduced fat', it must have at least 20% less fat than the regular item. what can conclude about how much fat is in a serving regular cookie?
Answers
Personally, I did this in a kinda weird way but I think that it should be correct
-How I figured the answer out-
I took 11g and wrote 80% next to it, because after all it has 80% less fat than the regular cookie.
Then, I scaled it down to 10% by dividing by 8, which got me
1.375g = 10%
And finally, I multiplied by 10 to now have 100% (meaning, a regular serving size cookie) and be left with the result: 13.75g
-The answer-
13.75g (don't forget to write the units)
Have a great day :)
Bernie bought a refrigerator at a special sale. The refrigerator regularly sold for $1296. No down
payment was required. Bernie has to pay $72 per month for 12 years. What is the average amount
Bernie pays in interest each month?
$0
$14.22
$17
ОО
$72
Answers
Answer:
$14.22 is the interest rate
What is the solution?
[tex]\lim_{x\to 0} \frac{x + 2}{ x -2}[/tex]
Math please
Answers
Answer:
[tex] - 1[/tex]
Step-by-step explanation:
[tex]\lim_{x\to 0} \frac{x + 2}{ x -2}[/tex]
[tex] = \frac{0 + 2}{ 0 -2}[/tex]
[tex] = \frac{2}{-2}[/tex]
[tex] = - 1[/tex]
Answer:
- 1
Ok? Understand?
........
Help I will give a lot of points and stuff
Answers
Answer:
x² - 20x - 12 = 0Step-by-step explanation:
One root is given, 10 - 4√7.
Since the polynomial has to have rational roots and of a minimal degree, the other root is the conjugate of the given and the polynomial is of degree 2 minimum.
The polynomial is:
(x - 10 - 4√7)(x - 10 + 4√7) = 0x² - (10 - 4√7 + 10 + 4√7)x + (10² - (4√7)²) = 0x² - 20x + 100 - 112 = 0x² - 20x - 12 = 04. Rhonda deposited $3000 in an account in
the Merrick National Bank, earning 4.2%
interest, compounded annually.
How much will she have in 5 years?
Answers
Answer:
Step-by-step explanation:
3000(1.042)^5= 3685.18970751
which rounds to 3685.19
PLEASE HELP WORTH 10
D. The expected height for someone with a femur length of 55 centimeters
Answers
Answer:
D. The expected height for someone with a femur length of 55 centimeters
From the sum of 4x² - 2x +6 and 2x² + 4x-1, subtract 5x2 + 2x -4.
Answers
Answer:
x² + 9Step-by-step explanation:
Add:
4x² - 2x + 6 + 2x² + 4x - 1 = 6x² + 2x + 5Subtract:
6x² + 2x + 5 - 5x² - 2x + 4 = x² + 9Answer: [tex]\large \boldsymbol {\sf x^2+9 }[/tex]
Step-by-step explanation:
[tex]1) \\\\ \large \boldsymbol {} \sf 4x^2-2x+6 \\ + \\ \underline{2x^2+4x-1} \\\\6x^2+2x+5[/tex] [tex]2) \\\\ \large \boldsymbol {} \sf 6x^2+2x+5 \\-\\ \underline{5x^2+2x-4} \\\\x^2+9[/tex]
Determine the slope of the line passing through the given points.
(1, 2) and (2, -1)
O m = -3
m = -1
m = -6
I m = 1
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
m = -3
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]m = \frac{\text{Change in Y}}{\text{Change in X}} = \frac{-1-2}{2-1} = \frac{-3}{1}=\boxed{-3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
What is the advantage of paying your credit card balance in full each month?
You will incur only a small "paid in full" fee on your next credit card statement.
You pay only a small amount of interest.
You have less of your credit limit available, therefore, less temptation to spend.
You avoid paying any interest and fees.
Answers
Answer:
D
You avoid paying any interest and fees, this is the most obvious since you are trying to avoid debt and fees which will build up as you don't pay them