I assume by f¹, you actually mean f⁻¹ as in the inverse of f. I also assume you are asked to find f(x) (as in the inverse of f⁻¹) and f⁻¹(4).
Given that
[tex]f^{-1}(x+2) = \dfrac{x-1}{x+1}[/tex]
with x ≠ 1, we can find f⁻¹(x) by replacing x + 2 with x :
[tex]f^{-1}(x + 2) = \dfrac{x-1}{x+1} = \dfrac{(x+2) - 3}{(x + 2) - 1} \implies f^{-1}(x) = \dfrac{x-3}{x-1}[/tex]
Then when x = 4, we have
[tex]f^{-1}(4) = \dfrac{4-3}{4-1} = \dfrac13[/tex]
Of course, we also could have just substituted x = 2 into the definition of f⁻¹(x + 2) :
[tex]f^{-1}(4) = f^{-1}(2+2) = \dfrac{2-1}{2+1} = \dfrac13[/tex]
To find f(x), we fall back to the definition of an inverse function:
[tex]f^{-1}\left(f(x)\right) = x[/tex]
Then by definition of f⁻¹, we have
[tex]f^{-1}\left(f(x)\right) = \dfrac{f(x)-3}{f(x)-1} = x[/tex]
Solve for f :
[tex]f(x) - 3 = x (f(x) - 1)[/tex]
[tex]f(x) - 3 = x f(x) - x[/tex]
[tex]f(x) - x f(x) = 3 - x[/tex]
[tex](1 - x) f(x) = 3-x[/tex]
[tex]f(x) = \dfrac{3-x}{1-x} = \dfrac{x-1}{x-3}[/tex]
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Answer:
See below
Step-by-step explanation:
Sine function would be easiest
in a right triangle sin = opposite leg / hypotenuse
sin 57 = 10.8 / x
then x = 10.8 / sin 57 then x = 12.88 units
The graph of which of the following will be perpendicular to the graph of y = 2x – 4? A. 2x + y = 4 B. 4x – 2y = 4 C. y = –2x + 8 D. 2x + 4y = 1 Please select the best answer from the choices provided
200 Points !!!!!!
The linear function that has a graph perpendicular to y = 2x – 4 is given by:
D. 2x + 4y = 1
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.If two lines are perpendicular, the multiplication of their slopes is of -1. The line y = 2x + 4 as a slope of 2, hence the slope of the perpendicular line will be given by m as such:
[tex]2m = -1[/tex]
[tex]m = -\frac{1}{2} = -0.5[/tex]
Hence option D is correct, as:
2x + 4y = 1
4y = -2x + 1
y = -0.5x + 0.25
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Solve for x:
e^(3x )+ e^x - 6 = 0
Right now I'm having trouble with the step u = e^x, u^3 + u - 6 = 0. Help!
The value of x of the cubic equation e³ˣ + eˣ - 6 = 0 will be 0.49
What is a cubic equation?The cubic equation is given as ax³ + bx² + cx + d = 0. Then degree of the equation will be 3. Then we have
The cubic equation will be
e³ˣ + eˣ - 6 = 0
Let eˣ = u, then the equation will be
u³ + u - 6 = 0
Then the root of the equation is calculated by the calculator, then we have
u = 1.634, -0.817, -0.817
eˣ = 1.634, -0.817, -0.817
Take log on both sides, then we have
x = ln 1.634, ln(-0.817), ln(-0.817)
x = 0.49, not defined, not defined
Then the value of x will be 0.49.
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If $3840 is deposited into a bank account at a 5% interest rate how long will it take the account to make $960 in interest?
assuming is simple interest
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$960\\ P=\textit{original amount deposited}\dotfill & \$3840\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 960 = (3840)(0.05)(t)\implies \cfrac{960}{(3840)(0.05)}=t\implies 5=t[/tex]
What is the answer to this math problem james works in a factory and wraps 8 packages every hour. how many hours will it take james to wrap 3,736 packages
By taking a quotient between the number of packages and the rate at which James works, we conclude that he will need 467 hours.
how many hours will it take James to wrap 3,736 packages?
We know that James wraps at a rate of 8 packages in one hour. Then to get the time in which he can wrap a number N of packages, we need to take the quotient between N and 8.
In this case, N = 3,736.
Taking the quotient we get:
3,736/8 = 467
This means that in 467 hours he will wrap the 3,736 packages.
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help meeee i need 100
How many times larger than (6 - 4) is (6 - 4) × 5?
Answer:
5 times bigger
Step-by-step explanation:
(6-4) = 2
(6-4) x 5 = 10
The only contents of a bag are 4 red balls and 6 blue balls. What is the probability that two balls drawn at random from the bag will be red if the first ball drawn is not replaced
Answer:
See below ~
Step-by-step explanation:
P (first red) :
⇒ Original number of red balls / Total
⇒ 4 / 10
⇒ 0.4
⇒ 40%
===============================================================
Remember the first ball drawn is NOT replaced.
P (second red) :
⇒ Original number of red - 1 / Total - 1
⇒ 4 - 1 / 10 - 1
⇒ 3/9
⇒ 33%
HELP PLEASE I WILL MARK BRAINLIEST
Solve for x: 3(x + 1) = −2(x − 1) − 4
1
−1
−5
−25
Answer:
x = - 1
Step-by-step explanation:
3(x + 1) = - 2(x - 1) - 4 ← distribute parenthesis on both sides
3x + 3 = - 2x + 2 - 4
3x + 3 = - 2x - 2 ( add 2x to both sides )
5x + 3 = - 2 ( subtract 3 from both sides )
5x = - 5 ( divide both sides by 5 )
x = - 1
find the 5th term of the GP is 48 and it 8th term is 384. find the first term and the common
Answer:
[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]
Step by step explanation:
[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]
Which addition does the model below represent?
5 positive tiles and 3 negative tiles.
Any time we have a single positive tile pair up with a single negative tile, those two tiles cancel out.
Three positive tiles and three negative tiles will pair up and cancel out. We're left with two positive tiles only. This represents the number 2.
In other words, 5 + (-3) = 5 - 3 = 2
2(z+5) +5(z+ 2) = 10(z − 1)
Answer:
z = 10
Step-by-step explanation:
First apply multiplication to inside the parenthesis:
2(z+5) = 2z + 10
5(z+ 2) = 5z + 10
10(z − 1) = 10z - 10 now write the full equation
2z + 10 + 5z + 10 = 10z - 10 add like terms
7z + 20 = 10z - 10 transfer like terms to the same side of the equation
20 + 10 = 10z - 7z
30 = 3z divide both sides by 3
10 = z
PLEASE SOLVE ITS UrgeNT I WILL MARK YOU BRAINLIEST! PLEASEE
Answer:B
Step-by-step explanation:
The amoeba splits 24 times, meaning that the number of amoebas will be
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 or 2^24
Assuming that there are no hidden cubes, what is the front orthographic view of the diagram?
Answer:
the visible number of cubes is 7
Step-by-step explanation:
Assuming that there are no hidden cubes, the # of visible cubes is 7
4. Factor:
j) x(x+2) + y (x + 2) - 5(x + 2)
k) 5y2 - 10y3
l) ax + ay + az
5. Factor:
m) yx(y+1) + 4x(y + 1) - 5(y + 1)
n) 6p2 - 3p3
o) 4x4 + 2x
The results of factoring are presented below for each algebraic expression.
x(x-3)+y(x+2)-105y²(1-2y)a(x+y+z)y(xy +5x-5)-13p²(2-p)[tex]2x(2x^3+1)[/tex]FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: y²-y= y(y-1), where y is a common term.
You should apply the factor out a common term for solving the question.
Exercise 4 - letter jx(x+2) + y (x + 2) - 5(x + 2)
x²+2x+xy+2y-5x-10
x²-3x+xy+2y-10
x(x-3)+y(x+2)-10
Exercise 4 - letter k[tex]5y^2 - 10y^3[/tex]
5y²(1-2y)
Exercise 4 - letter lax+ay+az
a(x+y+z)
Exercise 5 - letter myx(y+1) + 4x(y + 1) - 5(y + 1)
xy²+xy+4xy+4-5y-5
xy²+5xy-1-5y
y(xy +5x-5)-1
Exercise 5 - letter n[tex]6p^2 - 3p^3[/tex]
3p²(2-p)
Exercise 5 - letter o[tex]4x^4 + 2x[/tex]
[tex]2x(2x^3+1)[/tex]
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A 6-sided die is rolled.
Let A = rolling a 1
Let B = rolling an even number
Identify the probability of the following events.
*Write your answer as a fraction*
Answer:
Step-by-step explanation:
P(A∪B) = 1/6 + 1/2 = 2/3
Solving System of Equations Using Subtraction.
X + 4y = 11
X - 6y = 11
Answer:
x=11
y=0
Step-by-step explanation:
Don't know if this is what you're looking for but this is correct if you plug it in.
X + 4y = 11 Get x by itself. x=-4y+11 and plug it into the bottom.
X - 6y = 11
simplify -4y+11-6y=11
11-10y=11
-10y=0
y=0 plug it into the original and you will get
x=11
x=11
To properly use the Addition Property of Equality what number would have to be added in the equation, 14 = x - 6?
A -14
B 14
C -6
D 6
Addition Property of Equality is basically a complex way of saying add the same number to both sides. In this problem we are trying to isolate x for it to be by itself so we must deal with -6. Since we have -6 on one side we must use the "Addition Property of Equality" to add 6 to both sides which would cancel out the -6 and add 6 to 14.
Therefore, the option that best fits the description on what number we would have to use to get added in the equation would be option D, 6.
I start a walk at 2.47pm. The walk takes 85 minutes. What time does the walk finish?
Answer:
4:12pm
Step-by-step explanation:
85 minutes = 1 hour and 25 minutes
2:47pm + 1 hour 25 minutes = 3:72 pm
72 minutes = 1 hour 12 minutes so add another 1 hour to 3 and the balance is 12 minutes so walk ends at 4:12pm
Another way to look at it is as follows:
After 13 minutes, the time is 2:47 + 0:13 = 3pm
Remaining time left is 85-13 = 72 minutes = 1 hour: 12 minutes. Add that to 3pm and you get 4:12pm
Please Help if you know!
An equation that can be used to determine how much each cookie cost originally is ($13.32 + $7) / 16.
What is the equation that determines the cost of each cookie?
A coupon reduces the price of an item. Thus, the amount paid by Louis would be lower than the original price.
Original price = coupon + price paid
($13.32 + $7)
The cost per cookie, can be determined by dividing the original price by the total number of cookies bought.
($13.32 + $7) / 16
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Answer:
Step-by-step explanation:
Givens
Number of cookies = 16
Deduction = 7
Final Cost = 13.31
Equation
16c - 7 = 13.31
Solution
You are not asked for a solution but I'll put it here anyway.
16c - 7 = 13.32 Add 7 to both sides
16c -7+7 = 13.32+ 7 Combine
16c = 20.32 Divide by 16
16c/16 = 20.32/16
c = 1.27
Solve 3-212.
OA. x≤-30
OB. xs-18
OC. x≥-30
OD. x2-18
The solution of the inequality 3-x/2≥12 is x≤-18
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 3-x/2≥12
Three minus x by two greater than or equal to twelve
Subtract 3 from both sides
-x/2≥9
-x≥18
x≤-18
Hence, the solution of the inequality 3-x/2≥12 is x≤-18
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Ii
a survey asked 6,000 random college students about how they are paying for college.
one thousand students surveyed responded that they have taken out student loans.
which conclusion can be made about the population from this survey?
o a. most college students do not use students loans.
o b. half of college students are using students loans.
oc. one-quarter of college students are using students loans.
od. all college students are using students loans.
Answer:
Answer = most college students do not use students loans.
Step-by-step explanation:
To find the percentage of students taking out student loans we take 1,000/6000 to get roughly 17%. This is a very small number of students taking out student loans.
What is the perimeter of triangle JKL (same triangle as question #1)?
Answer:
x=30
Step-by-step explanation:
You have to use intercept theorem, also known as Thales's theorem to slvoe this.
15 Which point is a solution to the system below?
2y < -12x + 4
y <- 6x +4.
A (1,1)
B (0,6)
C (-1/2,5)
D (-3,2)
The attached graph shows that the system of equation has no solution since there is no point of intersection
Solution to system of equationsInequalities are expressions not separated by an equal sign
Given the following inequalities
2y < -12x + 4
y <- 6x +4
_________________
2y < -6x + 4
y <- 6x +4.
Find the y-intercept. When x = 0
y < -6(0) + 4
y < 4
Plot the graphs and determine the point of intersection
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Emma earned a grade of 95% on her multiple choice history final that had a total of
180 problems. How many problems on the final exam did Emma answer correctly?
Answer:
171
Step-by-step explanation:
180×95/100
180×95=17100
17100/100=171.
That is how I got my answer.
Find the slope of the line that passes through the points f(4) = 6 and f(-2) = 8.
Answer:
slope = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
given f(4) = 6 and f(- 2) = 8 , then 2 points on the line are
(4, 6 ) and (- 2, 8 )
calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (- 2, 8 )
m = [tex]\frac{8-6}{-2-4}[/tex] = [tex]\frac{2}{-6}[/tex] = - [tex]\frac{1}{3}[/tex]
Which set of ordered pairs has point symmetry with respect to the origin (0, 0)? (5, 4), (-5, -4) (5, 4), (5, -4) (5, 4), (4, 5) (5, 4), (-5, 4)
The set of ordered pair that has point symmetry in respect to origin is (5, 4), (-5, -4).
What is the point of symmetry?
This is a term that is used to refer to the points that are on the same distance from the origin but are on opposite sides.
The line that connects the points are known to move through the origin such that when measured on the graph, the distances between these points but they are opposite because they are in negatives and positives on the two sides.
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Answer:
the answer is (5,4),(-5,4)
Step-by-step explanation:
Draw a picture to show the value of 5 x (3 + 7)
How many times as big is 5 x (3 + 7) as (3 + 7)? How do you know?
Help please!!!!!!! I'm so confused about this
Answer: I think the answer is A (4,6)
Step-by-step explanation:
Because point B is translated up you have to move the whole shape and pint D would end up at (4,6)