Answer:
[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]
[tex]f(f^{-1}(x)) = f^{-1}(f(x))= x[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{2}{3}x - 6[/tex]
Required
Determine [tex]f^{-1}(x)[/tex]
[tex]f(x) = \frac{2}{3}x - 6[/tex]
Represent f(x) as y
[tex]y=\frac{2}{3}x - 6[/tex]
Swap the positions of x and y
[tex]x=\frac{2}{3}y - 6[/tex]
Add 6 to both sides
[tex]x+6=\frac{2}{3}y - 6+6[/tex]
[tex]x+6=\frac{2}{3}y[/tex]
Multiply both sides by 3
[tex]3(x+6)=\frac{2}{3}y * 3[/tex]
[tex]3(x+6)=2y[/tex]
Divide both sides by 2
[tex]\frac{3}{2}(x+6)=\frac{2y}{2}[/tex]
[tex]\frac{3}{2}(x+6)=y[/tex]
[tex]y= \frac{3}{2}(x+6)[/tex]
Replace y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]
Justify the result:
First, we solve for [tex]f(f^{-1}(x))[/tex]
[tex]f(x) = \frac{2}{3}x - 6[/tex]
[tex]f(x) = \frac{2}{3}x - 6[/tex] becomes
[tex]f(f^{-1}(x)) = \frac{2}{3}x - 6[/tex]
Substitute [tex]\frac{3}{2}(x + 6)[/tex] for x
[tex]f(f^{-1}(x)) = \frac{2}{3}(\frac{3}{2}(x + 6)) - 6[/tex]
[tex]f(f^{-1}(x)) = \frac{2*3}{3*2}(x + 6)- 6[/tex]
[tex]f(f^{-1}(x)) = \frac{6}{6}(x + 6)- 6[/tex]
[tex]f(f^{-1}(x)) = 1*(x + 6)- 6[/tex]
[tex]f(f^{-1}(x)) = x + 6- 6[/tex]
[tex]f(f^{-1}(x)) = x[/tex]
Next, we solve [tex]f^{-1}(f(x))[/tex]
[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex]
[tex]f^{-1}(x)= \frac{3}{2}(x+6)[/tex] becomes
[tex]f^{-1}(f(x))= \frac{3}{2}(x+6)[/tex]
Substitute [tex]\frac{2}{3}x - 6[/tex] for x
[tex]f^{-1}(f(x))= \frac{3}{2}(\frac{2}{3}x) - 6+6[/tex]
[tex]f^{-1}(f(x))= \frac{3}{2}(\frac{2}{3}x)[/tex]
[tex]f^{-1}(f(x))= \frac{2*3}{3*2}x[/tex]
[tex]f^{-1}(f(x))= \frac{6}{6}x[/tex]
[tex]f^{-1}(f(x))= 1*x[/tex]
[tex]f^{-1}(f(x))= x[/tex]
Hence:
[tex]f(f^{-1}(x)) = f^{-1}(f(x))= x[/tex]
Given f(x) = X-2 and g(x)= 1/x-2 which of the following values is not in the domain of (fog)(x)?
0
1/2
2
4
Answer:
The answer is 2
Step-by-step explanation:
Edge 2021
Given a standard deck of cards, what is the probability that you choose a red card and then choose a heart, assuming you replaced the first card?
A. 3/26
B 7/26
C 1/4
D 1/8
Arectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
x. y) x+5, y-3)
Oxy)- + 5.y + 3)
(K.)- K-3.y + 5)
(.)-(3.y+ 5)
Answer:
The first one x=5, y-3
Step-by-step explanation:
Look at the table
A 2-column table with 3 rows. Column 1 is labeled Animal with entries horse, pig, cow. Column 2 is labeled Number with entries 8, 6, 5.
What is the ratio of cows to horses?
to
.
Answer: 5:8
Step-by-step explanation:
There are 5 cows and 8 horses as outlined by the question. Thus, the ratio of horses to pigs is 5:8
Answer:
yeah as they said it is 5:8
3) The mean of a set of data is 4.68 and its standard deviation is 2.83. Find the z score for a value of 9.38.
Answer:
1.66
Step-by-step explanation:
The mean of a set of data is 4.68 and its standard deviation is 2.83. Find the z score for a value of 9.38
Given that :
Mean (m) = 4.68
Standard deviation (s) = 2.83
Value of x = 9.38
Zscore = (x - mean) / standard deviation
Zscore = (9.38 - 4.68) / 2.83
Zscore = 4.7 / 2.83
Zscore = 1.6607773
Hence, Zscore for a value of 9.38 is 1.66
NEED HELP PLEASE 16. A car dealer has 90 cars in the new car lot. The partially completed two-way table shown categorizes the cars by their color and whether or not they have backup
cameras. How many cars on the lot do not have backup cameras?
A. 45
B. 64
C. 53
D.8
Answer:
its 53. i just took the test
Step-by-step explanation:
6. A kennel has 90 dogs in total, some are puppies and some are adult dogs. The ratio of puppies to adult dogs in a kennel is 3 : 2. How many adult dogs are there?
Answer:
·ω·
Step-by-step explanation ·ω· thats it °ω°
Learning Task No. 3: Solve the following equation. Then compare
your answer by writing <, > and = in your notebook.
1.5 + 8 - 2 - 7
26 = 13 x 10 - 17
2. 22 x 3 - 42 + 20
72 - 2 + 13 - 16
3. 12 + 13 - 4 x 5
16 - 4 x 3 - 7
4. 45 - 10 x 2 + 17
16; 8 x 9-5 + 30
Answer:
(1) <
(2) <
(3) =
(4) <
Step-by-step explanation:
[tex]By \ applying \ the \ rule \ of \ BODMAS \ (i.e. \ Bracket, \ of, \ Division,\ Multiplication, \ Addition,[/tex][tex]\ and \ Subtraction).[/tex]
(1)
5 + 8 - 2 -7 = 13 × 10 - 17
13 - 9 = 130 - 17
4 < 113
(2)
22 × 3 - 42 + 20 = 72 -2 + 13 - 16
66 - 22 = 72 + 11 - 16
44 < 67
(3)
12 + 13 - 4 × 5 = 4 × 3 - 7
12 + 13 - 20 = 12 - 7
5 = 5
(4)
45 - 10 × 2 + 17 = 8 ×9 - 5 + 30
45 - 20 + 17 = 72 + 25
42 < 97
IF a= 6 and b= 7, then 4a(3b+5) + 2b =?
Answer:
64
Step-by-step explanation:
4a(3b+5)+2b
Substitution
4(6)[3(7)+5]+2(7)
Order of operations (PEMDAS)
4(6)[21+5]+2(7)
4(6)+26+2(7)
24+26+14
50+14
64
Hope this helps. Have a nice day. May it be filled with joy and happiness. Please, be safe and wash your hands. Happy Holidays.
What is grater -1.5 or -3/2
Answer:
the first on is greater
Step-by-step explanation:
please trust me
PLEASE HURRY FOR BRAINLIEST I BEG YOU!!
Answer:
5
Step-by-step explanation:
i did this before
An estimated 3 out of every 25 men are left-handed.
What percent of men are lert-handed?
Answer:
12%
Step-by-step explanation:
3 / 25 = 0.12
Move the dot 2 places to the right to get a percentage.
Answer:
12%
Step-by-step explanation:
3/25 * x/100
25x = 300
x=12
SOMEONE HELP ME THIS IS DUE TODAYYYY
PLZ RESPOND ASAP! 50 POINTS
classify which numbers are rational or irrational
The given numbers are:
5/4
√100
7.3
0.00247
√4/9
√2/24
0.01 with the line above the 1
Answer:
5/4 = rational √100 = rational 7.3 =rational 0.00247 = rational √4/9 = irrational √2/24 = irrational 0.01 (with the line) = irrational
Step-by-step explanation:
an irrational number is an infinitely repeating number that can not be written as a fraction, instead it must be written as a decimal. A rational number is a number that can be made by dividing two integers (an integer is a number with no fractional part).
The numbers are,
a. 5/4 = Rational
b. √100 = Rational
c. 7.3 = Rational
d. 0.00247 = Rational
e. √4/9 = Irrational
f. √2/24 = Irrational
g. 0.01 (with the line above the 1) = Irrational
What is Number system?
A system of writing to express the number is called number system.
Given that;
The numbers are,
5/4, √100 , 7.3 , 0.00247, √4/9 , √2/24 , 0.01 with the line above the 1.
Now,
Check the numbers as;
5/4 = 1.25
So, The number is a Rational number.
√100 = 10
So, The number is a Rational number.
7.3 = 7.3
So, The number is a Rational number.
0.00247 = 247/100000
So, The number is a Rational number.
√4/9 = 2/3 = 0.666.......
So, The number is a Irrational number.
√2/24
So, The number is a Irrational number.
0.01 with the line above the 1
So, The number is a Irrational number.
Thus, The numbers are,
a. 5/4 = Rational
b. √100 = Rational
c. 7.3 = Rational
d. 0.00247 = Rational
e. √4/9 = Rational
f. √2/24 = Irrational
g. 0.01 (with the line above the 1) = Irrational
Learn more about the Rational number visit:
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Simplify.
(+18)%(-6)
Answer: -3
Step-by-step explanation:
18/6 = 3
18/-6 = -3
Three times the number of polar bears is more than
twice the number of polar bears plus 45.
a. Write an inequality to model this situation.
b. Which of the following could possibly be the
number of polar bears?
A. 38
B. 40
C. 45
D. 48
Answer:
a. [tex]3x>2x+45[/tex] b. [tex]48[/tex]Step-by-step explanation:
For b the number of polar bears must be greater than 45 in order for there to be more on the left side.
Hope this helps! :)
Which number line shows -3, -2, 1, and 3 correctly plotted?
Answer:
i need a picture of the graphs
Step-by-step explanation:
need help with trig homework!
Enter the midpoint of the segment whose endpoints are (8, 7) and (-2, 16).
Answer:
(3, 11.5)
Step-by-step explanation:
The coordinates of midpoint are ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
( [tex]\frac{-2 + 8}{2}[/tex] , [tex]\frac{16+7}{2}[/tex] ) = ( 3 , 11.5 )
Answer:
(3, 11.5)
Step-by-step explanation:
midpoint=X1 + X2 , y1+y2
2 2
= 8 + (-2) , 7 + 16
2 2
= ( 6 /2 , 23/2)
= ( 3, 11.5)
what is value of expression 3x7+2^3/(3+1)
Answer:
The value of the expression is 23.
Step-by-step explanation:
3x7+2^3/(3+1) <----- Here is the original problem.
3x7+2^3/4 <----- Simplify what's in the parentheses.
21+2^3/4 <----- Do your multiplication (in the front)
21+8/4 <----- Simplify the exponent. (2 x 2 x 2 = 8)
21+2 <---- Do the division.
23 <----- Here is the correct answer.
Hope this helps! :D
Lee and Marisol are conducting a science experiment to identify different kinds of macromolecules in food. They prepare the following table to help them remember the chemical reactions that indicate the presence of each type of macromolecule they are studying.
Answer:
Step-by-step explanation:
License plates are made using letters followed by digits. How many plates can be made if repetition of letters and digits is allowed
How many plates can be made if repetition of leters and digits is allowed? 26*26*10*10=67,600 plates can be made.
this is what i looked up and got sry if its not
What are m and b in the linear equation 12 + 6x + 15 + 10x = y?
Answer:
m = 16
b = 27
General Formulas and Concepts:
Algebra I
Combining Like Terms
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
12 + 6x + 15 + 10x = y
Step 2: Simplify
Combine like terms (Z): 27 + 6x + 10x = yCombine like terms (x): 27 + 16x = yRewrite: y = 16x + 27Step 3: Identify
Break apart functions.
Slope m = 16
y-intercept b = 27
Five pirates share the treasure with Long John Silver. If the treasure is split, by weight, in the ratio 2:5:7:10:20:50, and the least amount any of the six pirates receives is 14,000 pounds of gold, what is the total weight of the treasure?
Answer:
658000
Step-by-step explanation:
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.
From the sample population of students with blond hair, what is the approximate value of the relative frequency of students with green eyes?
The required approximate value of the relative frequency of students with green eyes is 0.27. Option A is correct.
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
The population of the student having blond hair = 78
Total number of students with blond hair and green eyes = 21
Now,
Approximate value of the relative frequency of students with green eyes,
= 21 / 78
= 0.27
Thus, the required approximate value of the relative frequency of students with green eyes is 0.27. Option A is correct.
Learn more about Statistics here:
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I need help, also give explantion please
Answer:
[tex] \huge \: 8 {x}^{3} \times 3 {x}^{9} = 24 {x}^{12} [/tex]
Sydney bought three hams for three different prices. The prices were
$14.75, $12.25, and $21.11 How much did she spend in all? If
Sydney has $100 how much money does she have left over?
Answer:
She has 51.89
Step-by-step explanation:
if you add all those number up and then subtract it with 100 you get 51.89
If you mix the blue cheese and the cream cheese together, how many cups will there be in all? Write your answer as a reduced fraction in the form a/b. Type your answer with a space between the fraction and whole number.
_______cups?
this is the working
The answer will be one and three eighth cups
Step-by-step explanation:
hope this helps
The dispersion among sample means is less than the dispersion among the sampled items themselves becausea:______
a. Each sample is smaller than population
b. Very large value are averaged down
c. Sampled items are all drawn from the same population
d. None of thesee.
e. b and c
Answer:
The dispersion among sample means is less than the dispersion among the sampled items themselves because:______
b. Very large values are averaged down
Step-by-step explanation:
The sample means represent average values obtained from both large and moderate values. Through the process of averaging, the data values obtained as the sample means are much closer to the true values. This is why the dispersions among the sampled items will be larger than the dispersions among the sample means. Sample dispersions describe how spread out the data values are on the number line.
can anyone help me thanks
Answer:
b
Step-by-step explanation:
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