Answer:
[tex]inverse \ of \ f(x) : \frac{2x}{x-1}[/tex]
Step-by-step explanation:
[tex]y = \frac{x}{x-2}\\\\swap\ x\ and \ y\\\\x = \frac{y}{y-2}\\\\x(y -2) = y\\\\xy - 2x = y\\\\xy - y = 2x\\\\y(x-1)= 2x\\\\y = \frac{2x}{(x-1)}[/tex]
Step-by-step explanation:
Given two one-to-one functions f(x)f(x) and g(x)g(x) if
(f∘g)(x)=xAND(g∘f)(x)=x(f∘g)(x)=xAND(g∘f)(x)=x
then we say that f(x)f(x) and g(x)g(x) are inverses of each other. More specifically we will say that g(x)g(x) is the inverse of f(x)f(x) and
denote it by
g(x)=f−1(x)g(x)=f−1(x)
Likewise, we could also say that f(x)f(x) is the inverse of g(x)g(x) and denote it by
f(x)=g−1(x)
Given the function f(x)f(x) we want to find the inverse function, f−1(x)f−1(x).
First, replace f(x)f(x) with yy. This is done to make the rest of the process easier.
Replace every xx with a yy and replace every yy with an xx.
Solve the equation from Step 2 for yy. This is the step where mistakes are most often made so be careful with this step.
Replace yy with f−1(x)f−1(x). In other words, we’ve managed to find the inverse at this point!
Verify your work by checking that (f∘f−1)(x)=x(f∘f−1)(x)=x and (f−1∘f)(x)=x(f−1∘f)(x)=x are both true. This work can sometimes be messy making it easy to make mistakes so again be careful.
Explanation:
Setting y=f(x)
y=xx−2
this may be rearranged (intermediate steps shown) as follows
y(x−2)=x
x⋅y−2y=x
x⋅y−x=2y
x(y−1)=2y
x=2yy−1
This expression shows x in terms of y.
That is,
f−1(x)=2xx−1
Setting y=f(x)
y=xx−2
this may be rearranged (intermediate steps shown) as follows
y(x−2)=x
x⋅y−2y=x
x⋅y−x=2y
x(y−1)=2y
x=2yy−1
This expression shows x in terms of y.
That is, it is the inverse of function f(x).
That is,
f−1(x)=2xx−1
as required.
The Thompson’s went out to eat at the Cheesecake Factory. If their bill was $68.65 and they gave their server a 15% tip, how much did they pay altogether?
Answer:
$78.94
Step-by-step explanation:
15% = 0.15
multiply to the total (68.65)
0.15 × 68.65 = 10.2975
$68.65 + 10.2975 = $78.94
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What is the solution to the inequality |2n+5|> 1?
A)-3> n > -2
B)2< n <3
C)n<-3 or n>-2
D)n< 2 or n> 3
Answer:
C, n < –3 or n > –2
Step-by-step explanation:
In the figure GHF=EHD. Which statement it true brother CP CTC?
A) FH=HE
B) DH=HF
C) GH=HD
D) GF=HD
Answer: DH and HF correspond.
the corresponding side length of two similar polygons are 6cm and 15cm if the area of smaller polygon is 32cm^2 then what is the area of the larger triangle?
A parallelogram-shaped window is divided into two sections by a rectangular piece of wood. Find the total of the area of the surface.
The total area of the glass surface is _ square inches
Multiply mixed numbers 3 1/2 X 2 1/3
Answer:
8 1/6
Step-by-step explanation:
that is da answer bbbbb
Answer:
8 1/6
Step-by-step explanation:
3 1/2 X 2 1/3
7/2x7/3
+3x-4x what is the answer for this equation
Answer:
[tex]-x[/tex]
Step-by-step explanation:
[tex]3x-4x = -1x[/tex]
Hope this helps
Measurement question please show work thank you
Answers:
b) 92100 decimeters
c) 6650 decaliters
=====================================================
Work Shown for part b)
1 decameter = 10 meters
1 decimeter = 1/10 of a meter
10 decimeters = 1 meter .... multiply both sides by 10
100 decimeters = 10 meters ... multiply both sides by 10
100 decimeter = 1 decameter
921*(100 decimeter) = 921*(1 decameter)
92100 decimeters = 921 decameters
-------------------
Work Shown for part c)
We could follow the same idea as part b). I'm going to use another approach as shown in the diagram below. This conversion method is known as the railroad tracks method in some math textbooks.
Each column represents two things that are equivalent to one another. For example, 1 kiloliter is the same as 1000 liters. So each column, when you divide top over bottom, represents the value 1.
Notice the unit cancelations as shown by the color coding. The goal is to have every unit cancel except for the decaliters unit which is what we want to end up with ultimately.
Once you have the railroad tracks set up, you multiply straight across.
Along the top, we have 66.5*1000*1 = 66500
Along the bottom we have 1*10 = 10
Divide those results: 66500/10 = 6650
So 66.5 kiloliters converts to 6650 decaliters
Answer:
1) 92100 dm
2) 6650 decalitres
AIR TRAVEL - an airplane traveling at an altitude of 5,900m changes its altitude by - 2,900m. What does this change in altitude mean ?
Answer:
Step-by-step explanation:
altitude -2900 m means its height decreases by 2900 m or it comes down by 2900 m
A newsletter publisher believes that less than 49% of their readers own a laptop. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.10 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim
Answer:
The answer is "At the 0,10 level, there should be enough proof that the percentage is below 49%"
Step-by-step explanation:
Null and alternative hypothesis:
[tex]H_0 :P \geq 0.49\\\\H_1:P<0.49 \ \ (\text{Left tailed test})\\\\[/tex]
Significance level: [tex]\alpha = 0.10[/tex]
It is decided that the null hypothesis at the defined meaning level is rejected.
Can someone help me please
Step-by-step explanation:
you can follow the same procedure for others
The piecewise defined function f(x) is graphed below. What is the value of f(5)?
================================================
Explanation:
Draw a vertical line through 5 on the x axis. This represents the equation x = 5. Notice that we intersect the blue line at (5,-1) which tells us that f(5) = -1. There's a closed point here, meaning that the point is included. This is in contrast to the open hole at (5,3) which is not part of the function. So be careful not to say that f(5) = 3 because that's not the case.
Answer:
i think it's f(5) - a wild guess
Step-by-step explanation:
Solve for u.
U/-1 +-4=-1
U =
Answer:
U = -3
Step-by-step explanation:
U/-1 +-4=-1
Add 4 to each side
U/-1 +-4+4=-1+4
U / -1 = 3
Multiply each side by -1
U / -1 * -1 = 3* -1
U = -3
Find the value of x.
a
x = 104
b
x = 72.5
c
x = 166
d
x = 93.5
Answer:
x=104
Step-by-step explanation:
Angle Formed by Two Secants= 1/2(difference of Intercepted Arcs)
10.5 = 1/2( x-83)
Multiply each side by 2
2* 10.5 = 2*1/2( x-83)
21 = x-83
Add 83 to each side
21+83 = x-83+83
104 =x
Hope this help!!!
Have a nice day!!!
Thank you to the person that is helping me. I don’t understand this one at all..
Drag each shape to the correct category.
Identify which shapes are similar to shape A and which are not
8
7
6
15
4
1
3
2
1
-10-9
-7
-6
-5 -4
-3
-2 -1
1
2
3
4
5
6
28
9
10
-1
-2
-3
-4
17
-5
-6
Answer:
D- 456 is 3 2 7 4 = Ab
Step-by-step explanation:
How many questions were on Victoria test
Hello. Can anyone help me?
Type the correct answer in each box. The graph of a rational function is shown. Use the graph to approximate the key features. Enter coordinates as ordered pairs.
Answer:
horizontal asymptote : is 2
vertical : is -2
Y intercept: (0;2)
Consider two unique parallel lines. What aspects of these two lines are the same? What aspects of these two lines would have to be different?
HELPPP! Which answer.
A: It shows a positive correlation
B: It shows a negative correlation
C: It shows no correlation
D: As fouls increase, points decrease
Answer:
most likely C
Step-by-step explanation:
the overall shape the points make don't go in any particular direction other than sideways, so there doesn't seem to be a particular correlation
If you can please help me with this question~ the question is the image :)
Answer:
B
Step-by-step explanation:
Start by using the distance formula to find the raidus
The two points are (-2,1) and (-4,1)
√((-4+2)²+(1-1)²)= 2
The radius is two and we have our center which means we can write
(x+2)²+(y-1)²=4
now it's just a matter of expanding everyhting
x²+4x+4+y²-2y-3=0
x²+y²+4x-2y+1=0
This is equal to B
9. A parallelogram is formed by the supports
that attach a basketball backboard and rim to
the wall. The angles change as the basketball
apparatus is taken out and put away. If
ZDAB = 28º and ZADC = 7x + 26, solve for
X.
Answer:
X=18
Step-by-step explanation:
I got x=18 I don't have the work but I know it is right I have the key to a final review with that problem on it!
What is 15/5 simplified?
Answer:
3
Step-by-step explanation:
fractions are division, so if you divide the numerator by the denominator you'll always get the mixed number / whole number
so 3/4 is equal to 3 divided by 4
15 divided by 5 is 3, because 3 x 5 = 15
Find the nth term of the quadratic sequence
Answer:
x^2
Step-by-step explanation:
all the numbers are square roots so n square is the nth term.
2^2= 4
3^2=9
4^2=16
5^2=25
6^2=36
Answer:
[tex] {n}^{2} [/tex]
Step-by-step explanation:
Drawing number into triangular dot pattern and making a square (with same numbers of dots in rows and columns) will give a square number. Similarly, 16 = 42 = 32 + (3 + 3 + 1), 25 = 52 = 42 + (4 + 4 + 1) and so on.
A total of 3600 athletes partipated in the Singapore 2010 youth Olympic Games. There were 1200 media representatives who reported on the games, 20,000 volunteers who helped out during the games and 370,000 spectators who attended the games. Find the ratio of The number of media representatives to the number athletes to the number of spectators
Step-by-step explanation:
answer is in the image above
-[tex]- \frac{1}{5} xy -\frac{4}{5} xy[/tex]
paso por paso
Answer:
[tex]- \frac{1}{5} xy -\frac{4}{5} xy \\ = { \tt{( - \frac{1}{5} - \frac{4}{5} )xy }} \\ \\ = { \tt{ - xy}}[/tex]
Round your answer to one decimal digit. The volume of a cylinder is 1 800 cm3. If the height of the cylinder is 40 cm then the diameter of the cylinder is
Answer:
7.57 cm
Step-by-step explanation:
Volume of a cylinder = πr²h
π = 3.14
r= radius
h = height
1,800 = 3.14 x r² x 40
r² = 1800 /(3.14 x 40)
r² = 14.33121
√14.33121 = r
r = 3.785658 cm
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
Diameter = 2 x 3.785658 cm = 7.57cm
Which undefined term is used to define an angle?
line
plane
point
ray
The undefined term is point.
What is an angle?In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle. Let us read about the different parts of an angle.
Parts of an Angle
There are two main parts related to an angle - the arms and the vertex.
Arms of the Angle
The two rays which join at a common point to form the angle are called the arms of the angle. Observe the figure given below which shows that OA and OB are the arms of the angle AOB.
[tex]vertex[/tex]of the angle
[tex]vertex[/tex] is a common endpoint that is shared by the two rays. Observe the figure in which the [tex]vertex[/tex] O is marked as the joining point of the two arms.
Measure of an angle
An angle is measured in degrees. One full rotation around a point forms a complete angle of 360°.
As, the is defined on the basis of arms , vertices, measurement.
They all related to point and point doesn't have a particular definition.
Learn more about angle here:
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what two numbers multiply to -78 and add to -7
546 Is The Answer
#KeepOnLearning
Answer:
13 and -6 or 6 and -13
Step-by-step explanation:
Use systems of equations
Find all x-intercepts of the function. Express your answer as a list of x-values.
f(x)=x ^5-3x^3
Answer:
[tex]x=0[/tex] and [tex]x=\pm\sqrt{3}[/tex]
Step-by-step explanation:
[tex]f(x)=x^5-3x^3[/tex]
[tex]0=x^5-3x^3[/tex]
[tex]x^5-3x^3=0[/tex]
[tex]x^3(x^2-3)=0[/tex]
[tex]x^3=0[/tex] and [tex]x^2-3=0[/tex]
[tex]x=0[/tex] and [tex]x=\pm\sqrt{3}[/tex]
See the graph for a visual of the x-intercepts.
