We should confirm that f(x) has an inverse in the first place. If it does, then
[tex]f\left(f^{-1}(x)\right) = x[/tex]
Given that f(x) = x/(2 - x), we have
[tex]f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)}{2 - f^{-1}(x)} = x[/tex]
Solve for the inverse:
[tex]\dfrac{f^{-1}(x)}{2 - f^{-1}(x)} = x[/tex]
[tex]f^{-1}(x) = 2x - x f^{-1}(x)[/tex]
[tex]f^{-1}(x) + x f^{-1}(x) = 2x[/tex]
[tex]f^{-1}(x) (1 + x) = 2x[/tex]
[tex]f^{-1}(x) = \dfrac{2x}{1+x}[/tex]
Then
[tex]f^{-1}(-2) = \dfrac{2(-2)}{1-2} = \boxed{4}[/tex]
Note that this is the same as solve for x when f(x) = -2 :
x/(2 - x) = -2 ⇒ x = 4
Find the Mean of the given data. 10,20,30,40,50
Answer:
The mean is 30
Step-by-step explanation:
To find the mean you add up all the numbers then divide how many numbers there are.....
10+20+30+40+50=150
150/5= 30
Hope this helps<3
A bank balance is more than $35. Julia wants to write an inequality for the bank balance. Which inequality symbol should she use to match the phrase “more than”?
Plus
Greater-than
Less-than
Times
Answer:
x>35
Step-by-step explanation:
The inequality symbol she should use to match the phrase “more than” is "Greater-than".
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
A bank balance is more than $35.
Let x represents the bank balance.
So, if the bank balance is more than $35,
x > 35
The symbol used is "greater than".
Hence the symbol used for the given inequality expression is "greater than".
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what is 685 x 32?? im confused
Answer:
21920
Step-by-step explanation:
Answer:
21,920
Step-by-step explanation:
Work uploaded below :)
Florida had a sales rate of 6 percent, and Gainesville has a sales tax of 1 percent. What is the total of the state sales tax and the city tax?
I'm thinking 5.95% sorry if I'm wrong
The table shows values for functions f(x) and g(x). X f(x)=4x 1 g(x)=3x 1−4 −3 −11 −359 −2 −7 −113 −1 −3 −3 0 1 −1 1 5 5 2 9 23 3 13 77 What is the solution to f(x)=g(x) ? Select each correct answer. −3 −2 −1 0 1 2 3.
f(x) = g(x) at 0 and 1.
FunctionThe function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Given
x f(x) = [tex]\rm 3^x[/tex] g(x) = 2x + 1
-2 [tex]\frac{1}{9}[/tex] -3
-1 [tex]\frac{1}{3}[/tex] -1
0 1 1
1 3 3
2 9 5
To findThe solution to f(x)=g(x).
How to find the solution to f(x)=g(x) ?It is clear that at x = 0 and 1, f(x) = g(x).
Thus, f(x) = g(x) at 0 and 1.
More about the function link is given below.
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Hey There!
Solve For x ~
[tex] \large\sf \: 4x + 2 = -8?[/tex]
Thank You! :)
Hope It's Helps! :)
The value of x in the algebraic expression is -2.5
What is an algebraic expression?An algebraic expression is the representation of numbers with variables with the purpose of solving for the variable. The variables are expressed by using alphabetical letters, here it is (x).
From the given algebraic expression, we have:
4x + 2 = -8
Collect like terms
4x = -8 - 2
4x = - 10
Divide both sides by 4
[tex]\mathbf{\dfrac{4x}{4} = \dfrac{-10}{4}}[/tex]
x = -2.5
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Find the measure of the arc. *
X
42°
V
W
?
O 42 degrees
84 degrees
0 21 degrees
O 81 degrees
The measure of the intercepted arc is: B. 84°.
The Inscribed Angle TheoremBased on the inscribed angle theorem, if an inscribed angle measures A, and the intercepted arc measures B, therefore, A = 1/2(B).
Thus, given the following:
Inscribed angle = 42°intercepted arc = WV = ?Thus:
42 = 1/2(WV)
WV = 2(42)
WV = 84°
Therefore, the measure of the intercepted arc is: B. 84°.
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r= 4/3(p-q)
solve for p
Answer = p=12-4 -12=17=18+19
p-q
p=12
what is the history of Saint Valentine's Day
Answer:
Because he died on that day
Step-by-step explanation:
Help me with my math homework
Which linear inequality is represented by the graph?
is the equation y = x2 - 8 linear or nonlinear? show work or explain
Answer:
linear
Step-by-step explanation:
nonlinear equations have exponents and linear equations do NOT have exponents .
Find the slope on the line
Answer:
-1
Step-by-step explanation:
Use Rise/Run and since the line is negative the slope will be negative
tom buys call of duty for $49.99 and also trades in a game for a credit of $5.60. There is no tax and he pays with a $100 bill. What is his change?
Tom has $25 saved and saves $3 a week Jim has 100$ saved and spends $12 a week . When will they have the same amount in their bank accounts
tom= 25 + 3x
jim = 100 - 12 x
100 -12x = 25 + 3x
75 = 15x
x = 5
after 5 weeks they will have the same amount in their bank accounts
HELP ME PLEASE I DONT UNDERSTAND THIS !!!
A certain car going 60 mph can stop in 180 ft. At what speed is the car traveling if it can stop in 100 ft?
The car is speeding at a rate of 33.3mph
Speed and distance of an objectIf a certain car going 60 mph can stop in 180 ft, then we can express this as:
60mph = 180ftTo determine the speed for a car traveling at 100ft, we will have:
x = 100ftTake the ratio of the expression
60/x = 180/100
180x = 6000
x = 33.3mph
Hence the car is speeding at a rate of 33.3mph
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Feb 03, 11:54:47 PM
Solve for the value of n.
(n+6°
(2n+3)
Bu
Answer: n =
Submit Answer
attempt 1 out of 2
I could be wrong here
n+6=2n+3
Subtract n from n+6 and subtract n from 2n+3 to get 6=n+3
Subtract 3 from both sides to end up with n = 3
?
Question 1 of 25
In preparing for his group's party, Ozzie cut up 26 strawberries. Then he answered a phone call. After the call, he cut up 18 more strawberries. How many strawberries did Ozzie cut up?
A. 26 strawberries
B. 34 strawberries
C. 8 strawberries
D. 44 strawberries
Please explain 12 and13and please please please hurry!
Answer:
12. a = 2
13. [tex] x = \dfrac{4}{3} [/tex]
Step-by-step explanation:
12.
6a(a + 3) = 2a(3a + 5) + 16
First, distribute 6a on the left side, and distribute 2a on the right side.
6a² + 18a = 6a² + 10a + 16
Subtract 6a² from both sides.
18a = 10a + 16
Subtract 10a from both sides.
8a = 16
Divide both sides by 8.
a = 2
13.
[tex] \dfrac{1}{3}x + \dfrac{1}{2}x = \dfrac{1}{3}(x + 2) [/tex]
The LCD of 2 and 3 is 6. We multiply both sides of the equation by 6 to get rid of all denominators.
[tex] 6 \times \dfrac{1}{3}x + 6 \times \dfrac{1}{2}x = 6 \times \dfrac{1}{3}(x + 2) [/tex]
[tex] \dfrac{6}{3}x + \dfrac{6}{2}x = \dfrac{6}{3}(x + 2) [/tex]
[tex] 2x + 3x = 2(x + 2) [/tex]
Combine like terms on the left side. Distribute the 2 on the right side.
[tex] 5x = 2x + 4 [/tex]
Subtract 2x from both sides.
[tex] 3x = 4 [/tex]
Divide both sides by 3.
[tex] x = \dfrac{4}{3} [/tex]
A data set has a maximum of 84, a minimum of 34, a median of 52.5, an upper quartile of 64, and a lower quartile of 44. Which statement is true of the box plot of this data set? The box will go from 44 to 64.A line dividing the box will be at 54.The left whisker will go from 34 to 52.5.The right whisker will go from 44 to 84.
Answer:
The box will go from 44 to 64.
Step-by-step explanation:
A box plot shows the five-number summary of a set of data.
Given five-number summary:
Minimum = 34Lower quartile (Q₁) = 44Median (Q₂) = 52.5Upper quartile (Q₃) = 64Maximum = 84To represent the given data as a box plot:
Draw a box from the lower quartile (44) to the upper quartile (64).Draw a vertical line through the box at the median (52.5).Draw horizontal lines (whiskers) from the lower quartile (44) to the minimum value (34) and from the upper quartile (64) to the maximum value (84).(See attached for box plot).
Therefore, the true statement is:
The box will go from 44 to 64.
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Answer: The box went from 44 to 64
Step-by-step explanation:keep it simple
Por qué crees que el valor de la media no aparece en la tabla y es un número decimal?
La media no aparece en la tabla ya que se requiere un calculo para encontrarla, además, es un número decimal pues corresponde a la suma de los resultados dividida en el número de días.
¿Qué es la media?En matemáticas, la media o promedio corresponde a la suma de todos los valores dividida en el número total de valores. En este caso la media corresponde a la suma de las temperaturas dividida en el número de días.
Calcular la media:
Usando la formula anterior, calculemos la media:
16 + 19 +17 + 20 + 22 + 18 +15 = 127/7 = 18.7El valor de la media es 18.7, al respecto se puede observar que:
Este valor no aparee en la tabla pues no corresponde a la temperatura de ningún día sino que debe ser calculado.Este valor es decimal, lo que se común al hallar la media ya que se suman todos los valores y se dividen por un número determinado.Nota: Esta pregunta esta incompleta. Aquí esta la parte faltante:
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can someone help me please
A slide 5.1 m long makes an angle of 35° with the ground. To the nearest tenth of a meter, how
far above the ground is the top of the slide?
A: 3.6m
B: 2.9m
C: 4.2m
D: 7.3m
The top of the slide is 2.9 meters far above from the ground.
The correct option is B.
What is a sine function?The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.
Given:
A slide 5.1 m long makes an angle of 35° with the ground.
Let the top of the slide is x meters far above from the ground.
Sin(35°) = Opposite/Hypotenuse
Sin(35°) = x / 5.1
x = (5.1) Sin(35°)
x = 2.92 meters.
Therefore, the distance is 2.92 meters.
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What is the slope of the line
Answer:
-2
Step-by-step explanation:
you are given that 3y=5x
find the value of when x=12
Answer:
60 is the answer
Step-by-step explanation:
Choose 10 whole numbers AND 10 decimals. Calculate 10% for all 20 numbers. Then, describe the pattern that you notice. Repeat for 1%.
Solve pls brainliest
Answer:
-54 and 56
Step-by-step explanation:
An integar is only the number which has no decimals or fractions
Identify the property demonstrated:
(5^3)^2 =5^3⋅2
A. Quotient of Powers Property
B. Power of a Product Property
C. Product of Powers Property
D. Power of a Power Property
Answer:
D. Power of a Power Property
Step-by-step explanation:
have great day :D
Please help me with this quick!
the picture is above
I’ll make you brainly
Answer:
The answer is A, C, and D
Step-by-step explanation:
Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a heart and the second card is red
Answer:
25/208 or 12.2%
Step-by-step explanation:
P(heart) = 13/52 = 1/4
P(red) = 26/52 = 1/2
because we are not replacing the first card drawn, the deck has 51 cards remaining
P(heart, red) = 1/4 × 25/52
= 25/208 or 12.2%
