Find the inverse of each function
1. f(x) = 4/(x+2) - 2
2. f(x)= -2x^5 - 3
Answers
9514 1404 393
Answer:
1. f^-1(x) = 4/(x+2) -2
2. f^-1(x) = (-(x+3)/2)^(1/5)
Step-by-step explanation:
1. As with all "inverse function" problems, solve for y:
x = f(y)
x +2 = 4/(y +2) . . . . add 2
y +2 = 4/(x +2) . . . . . multiply by (y+2)/(x+2)
y = 4/(x+2) -2 . . . . . subtract 2
We see that this function is its own inverse. The attached graph shows it is symmetrical about the line y=x.
f^-1(x) = 4/(x+2) -2
__
2. x = f(y)
x +3 = -2y^5 . . . . add 3
-(x +3)/2 = y^5 . . . . . divide by 2
(-(x +3)/2)^(1/5) = y . . . . take the 5th root
f^-1(x) = (-(x +3)/2)^(1/5)
In typeset form, that is ...
[tex]\displaystyle f^{-1}(x)=\sqrt[5]{\frac{-(x+3)}{2}}\\\\\text{or}\\\\f^{-1}(x)=-\frac{1}{2}\sqrt[5]{16x +48}[/tex]
This last version is with the denominator "rationalized" and the contents of the radical "simplified." It may be a preferred form.
_____
The graphs show the function and inverse are symmetrical about the line y=x, as they should be.
Related Questions
Please can anyone answer this question
Answers
Not 100% sure tho
A farmer used 204 feet of fencing to enclose a garden in the shape of a rectangle. If the length of the garden is twice the width, what is the width of the garden?
A) 34ft
B) 40.8ft
C) 51ft
D) 68ft
E) 81.6ft
Answers
Answer:
A
Step-by-step explanation:
Area=L+L+B+B
L=2
B=1
So, L+L+B+B=6
204/6=34
So, it's 34 ft, which is A.
X = {1,3,5,7)
Y = {13,57}
Which of the following is the set XnY?
Answers
Answer:x is a letter in music.} 3. Determine whether each set is well-defined. If it is not well-defined, explain why, ... true (e) {1, 3, 5, 7, 9) = {1, 5, 9, 3, 7) false_(f) {1,3,5, 9) = {1,3,5,9} ... Describe each of the following sets as either finite or infinite. ... 13 listened to heavy metal and alternative rock; 12 listened to rap and alternative rock;. or
x 2 - 2yZ = 7 with x = 2v + 1 and y = 2b + 1. These have solutions. (x, y; v, b) = (3, 1; 1,0), (5,3; 2,1), (13,9; 6,4),. (27,19; 13,9), (75,53; 37, 26), (157,111; 78, 55), .
Step-by-step explanation:
simplify 8x+7-x-4
help meeeeee!!!
Answers
Answer:
7x + 3
Step-by-step explanation:
Let's simplify step-by-step.
8x + 7 − x − 4
= 8x + 7 + −x + −4
Combine Like Terms:
= 8x + 7 + −x + −4
= (8x + −x) + (7 + −4)
= 7x + 3
Answer:
= 7x + 3
hope this helps and is right. p.s i really need brainliest :)
if my answer is wrong then I am incredibly sorry!
Solve 3y^3 + 12y^2 + 12y =0
Please
Answers
Answer:
y = 0, -2
Step-by-step explanation:
Factor out the common term 3y.
[tex]3y( {y}^{2} + 4y + 4) = 0[/tex]
Rewrite y² + 4y + 4 in the form of a² + 2ab + b², where a = y and b = 2.
[tex]3y( {y}^{2} + 2(y)(2) + {2}^{2} ) = 0[/tex]
Use square sum: (a + b)² = a² + 2ab + b².
[tex]3y(y + 2) ^{2} = 0[/tex]
solve for y.
y = 0, -2.
therefor, the answer for this equation is 0, - 2.
for triangle ABC with sides a,b and c the law of cosines states
c^2=
in which of the following cases must the law of cosines be used to solve a triangle?
ASA SSS SAS SSA
Answers
Option C is correct. The law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)
For a triangle, ABC with sides a, b, and c respectively, the law of cosines is used on such a triangle if there is a presence of an angle between any two sides.
For example, if angle C is between the sides a and b, the equivalent cosine rule will be expressed as:[tex]c^2 = a^2 + b^2 + 2ab cos C[/tex]
Hence the law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)
Learn more here: https://brainly.com/question/20880990
Evaluate the expression [(18 ÷ 2 + 54 ÷ 9) × 2] × 2.
PLEASE EXPLAIN I KNOW ITS 60
Answers
Answer:
PEMDAS
Step-by-step explanation:
Answer:
[tex]=60[/tex]
Step-by-step explanation:
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex].
[tex]\left(18\div \:2+54\div \:9\right)\times \:2[/tex]
[tex]=15\times \:2[/tex]
[tex]=30[/tex]
[tex]=30\times \:2[/tex]
[tex]=60[/tex]
Find 3 consecutive even integers such that 5 times the second is 82 more than the first .
Answers
Ti best of my understanding the answers are: 1st integers is 18, 2nd is 20, and 3rd is 22.
x is 1st integer
x+2 is 2nd integer
x+4 is 3rd integer
All even
5(x+2)=82+x
5x+10=82+x
5x-x=82-10
4x=72
x=18
1st is x=18
2nd is x+2=18+2=20
3rd is x+4=18+4=22
Good luck.
What fraction is equivalent to 10 and has a denominator of 100? (2 points)
6
100
7
60
100
o
600
100
a
60
10
Answers
Answer:
1000 / 100
Step-by-step explanation:
Answer:
ff
Step-by-step explanation:
40 pts please help!
Find the circumference and area of a circle with a diameter of 7cm. Round your answers to the hundredth.
a. C = 21.98cm and A = 38.47cm squared
b. C = 21.98cm and A = 153.86cm squared
c. C = 43.96cm and A = 38.47cm squared
d. C = 43.96cm and A = 153.86cm squared
Answers
Answer:
a.
Step-by-step explanation:
diameter 7cm
radius 3.5cm
area =πr²
=22/7* 3.5²
=38.47cm²
circumference=πd
=22/7* 7
=22cm
Answer:
a. C = 21.98cm and A = 38.47cm squared
Step-by-step explanation:
Diameter is twice the radius. Therefore radius, r, is 3.5cm.
Circumference = 2πr =2π(3.5)=7π=21.98cm
Area=πr²=π(3.5²)=12.25π=38.47cm²
10 POINTS FOR THE CORRECT ANSWER PLEASE HELP ME
Answers
Answer:
x = 10
Step-by-step explanation:
I made a right triangle with a leg of 6 (7-1), base of 7, and hypotenuse of 'x' and then used the pythagorean theorem:
6² + 8² = x²
100 = x²
x = √100
x = 10
What percent of the cars passed through between 2pm and 2:59 pm
Answers
Answer:
Can you actually do your own work
Step-by-step explanation:
Do it yourself
Please help asap please help
Answers
Answer:
C. 40 + (-58) + 160Step-by-step explanation:
It would be easier with C., the other options are already easy to calculate
40 + (-58) + 160 = 40 + 160 + (-58) = 200 - 58 =142Birth control pills have a theoretical annual efficacy of 99.5%, but a real-worls efficacy of only 95%. If a college student takes the pill for the four years she is in college, what is the probability that she will become pregnant at least once using the theoretical efficacy rate?
A. 0
B. 0.005
C. 0.020
D. 0.185
Answers
Answer:In my opinion B.0.005 is the correct answer
Step-by-step explanation:
hope it will help you
What is the mean for these numbers?
5,5,5,5
Answers
Answer:
IF THERE IS A LINK DON'T CLICK ON IT
Step-by-step explanation:
IT'S A COMPUTER PHONE AND TABLET VIRUS
Answer:
5
Step-by-step explanation:
Sin 17° cos 13° + cos 17° sin 13°
Answers
Answer:
.5
Step-by-step explanation:
Sin(x)cos(y) + cos(x)sin(y) = sin(x+y)
sin(17+13) = 1/2
A factory received a shipment of 11 hammers, and the vendor who sold the items knows there are 2 hammers in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the hammers in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places
Answers
Question:
If a sample of 2 hammer is selected
(a) find the probability that all in the sample are defective.
(b) find the probability that none in the sample are defective.
Answer:
a [tex]Pr = \frac{2}{110}[/tex]
b [tex]Pr = \frac{72}{110}[/tex]
Step-by-step explanation:
Given
[tex]n = 11[/tex] --- hammers
[tex]r = 2[/tex] --- selection
This will be treated as selection without replacement. So, 1 will be subtracted from subsequent probabilities
Solving (a): Probability that both selection are defective.
For two selections, the probability that all are defective is:
[tex]Pr = P(D) * P(D)[/tex]
[tex]Pr = \frac{2}{11} * \frac{2-1}{11-1}[/tex]
[tex]Pr = \frac{2}{11} * \frac{1}{10}[/tex]
[tex]Pr = \frac{2}{110}[/tex]
Solving (b): Probability that none are defective.
The probability that a selection is not defective is:
[tex]P(D') = \frac{9}{11}[/tex]
For two selections, the probability that all are not defective is:
[tex]Pr = P(D') * P(D')[/tex]
[tex]Pr = \frac{9}{11} * \frac{9-1}{11-1}[/tex]
[tex]Pr = \frac{9}{11} * \frac{8}{10}[/tex]
[tex]Pr = \frac{72}{110}[/tex]
HELP ON HOMEWORK PLS
Answers
Answer:
∠LPN = 57°
Step-by-step explanation:
arc LMN = 360° - 102° - 144° = 114°
∠LPN = 114°/2 = 57°
Doors for the small cabinets are 11.5 inches long. Doors for the large cabinets are 2.7 times as long as the doors for the small cabinets. How many large doors can be cut from a board that is 10 feet long?
Answers
Answer:So if you take the small cabinet door length which is 11.5 inches long and multiply by a factor of 2.3 you get the total length of the large cabinet doors, which is 26.45 inches
Step-by-step explanation:
Determine if the expression -1−1 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answers
Answer:
Determine if the expression -1−1 is a polynomial or not. If it is a polynomial, state the type and ... - did not match any documents.
Suggestions:
Make sure that all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords.
Need help!!!!!!!!!!!
Answers
Answer:
90°
-Sum of angles in a triangle= 180°
-angle C is 90°
-therefore angle A + angle B is,
180° - 90° = 90°
Choose all of the statements that correctly compare the two functions shown.
Alec's rate of savings is greater than Beth's.
entific
Alec and Beth are saving at the same rate.
Alec started with more money than Beth
mulas
Time
maining
:19:23
Beth started with more money than Alec,
de les
At 10 days, Alec will have $1 more than Beth in savings,
Answers
Answer:
b, c and e
Step-by-step explanation:
Given
See attachment for functions
Required
Select all statements that contain both functions
First, calculate the rate (slope) of both functions.
This is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For Alec's
[tex](x_1,y_1) = (0,3)[/tex]
[tex](x_2,y_2) = (2,9)[/tex]
So, the slope is:
[tex]m = \frac{9 - 3}{2 - 0}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m =3[/tex]
For Beth's
[tex](x_1,y_1) = (5,17)[/tex]
[tex](x_2,y_2) = (12,38)[/tex]
So, the slope is:
[tex]m = \frac{38 - 17}{12 - 5}[/tex]
[tex]m = \frac{21}{7}[/tex]
[tex]m =3[/tex]
Beth and Rec have the same slope. Hence, they save at the same rate.
Next, determine the amount they started with.
This implies that we calculate y when x = 0
From Alec's graph.
[tex](x,y) = (0,3)[/tex]
Alec's initial savings is 3
For Beth's savings, we make use of slope formula.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex](x_1,y_1) = (5,17)[/tex]
[tex](x_2,y_2) = (0,y)[/tex]
So, we have:
[tex]3 =\frac{y - 17}{0 - 5}[/tex]
[tex]3 =\frac{y - 17}{ - 5}[/tex]
[tex]y - 17 = -15[/tex]
[tex]y = 17 -15[/tex]
[tex]y = 2[/tex]
Beth's initial savings is 2
Hence, Alec started with more money
Next, is to determine who has more money after 10 days.
Since they save at the same rate, the difference in their savings after any number of days will be the difference in their initial savings.
The difference (d) is calculated as:
[tex]d = 3 - 2[/tex]
[tex]d = 1[/tex]
Hence, Alec will have $1 more than Beth after 10 days
Answer:
its bc and e or Alec and Beth are saving at the same rate. Alec started with more money than Beth. and At 10 days, Alec will have $1 more than Beth in savings.
Step-by-step explanation:
Please help me ASAP please
Answers
Answer:
Step-by-step explanation:
the first sounds like J/9=5, which in an equaiton could be written as 5=j/9.
Then to solve for j you can multiply both sides by 9. This would create j=45. Hopefully this is helpful!
Answer:
[tex]\frac{j}{9}[/tex] = 5 is the equation, j = 45 is the answer.
Step-by-step explanation:
J divided by 9 is 5.
[tex]\frac{j}{9}[/tex] = 5.
Multiply by 9 to find the answer.
j = 5 * 9
j = 45.
Solve for x.
5(x + 1) = 4(X + 8)
Ox= 37
Ox=7
Ox=27
Ox=17
Help please
Answers
Answer:
27
Step-by-step explanation:
What three-dimensional figure is represented by the net shown below?
A cube
B square pyramid
C rectangular prism
D rectangular pyramid
Answers
Answer:
C
Step-by-step explanation:
The net, if you imagine it folded up, will look like a long box.
Because all the dimensions are not equal, the figure cannot be a cube. Both square and rectangular pyramids have 5 faces, unlike this net.
A net of a rectangular prism, however, will have different dimensions for [tex]l[/tex] and [tex]w[/tex], and have 6 faces. So, the answer is C, rectangular prism.
Good luck ^^
The three-dimensional figure represented by the net shown below is a rectangular prism.
Option C is the correct answer.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
From the figure,
We see that it is an open rectangular prism.
All the open sides are rectangular in shape.
If we fold all the sides it will form a rectangular prism.
Thus,
The three-dimensional figure represented by the net shown below is a rectangular prism.
Learn more about prism here:
https://brainly.com/question/12649592
#SPJ2
What is the average rate of change for this exponential function for the
interval from x = 0 to x = 2?
A. -1.5
B. -4
C. 1.5
D. 4
Answers
Answer:
C i hope it helps
have a good night
The mean age at which the population of babies first stand without support is normally distributed with a mean of 13.20 months with a standard deviation of 2.00 months. What is the probability of randomly selecting a sample of 25 children who stood on their own by the average age of 12.2 months or earlier
Answers
Answer:
0.00621
Step-by-step explanation:
We solve the above question using the
Z score formula. This is given as:
z = (x-μ)/σ/√n
where
x is the raw score = 12.20 or earlier
This means x ≤ 12.20
μ is the population mean = 13.20
σ is the population standard deviation = 2
n is the random number of samples = 25
z = 12.2 - 13.2/2/√25
z = -1/2/5
z = -1/0.4
z = -2.5
Probability value from Z-Table:
P(x≤ 12.2) = 0.0062097
Approximately = 0.00621
Therefore, the probability of randomly selecting a sample of 25 children who stood on their own by the average age of 12.2 months or earlier is 0.00621
the perimeter of a rectangle is 36cm.If it is length is 10 cm find its breadth
Answers
Answer:
The perimeter of a rectangle is 36 cm, its breadth is 8 cm
Step-by-step explanation:
For a given rectangle
Perimeter (P) = 36 cm
length (L) = 10 cm
Now,
Perimeter (P) = 2 × (length + breadth)
P = 2 × (l + b)
36 = 2 × (10 + b)
36 = 20 + 2b
2b = 36 - 20
2b = 16
b = 16 ÷ 2
b = 8 cm
Thus, The perimeter of a rectangle is 36 cm, its breadth is 8 cm
-TheUnknownScientist
The perimeter of a rectangle is 36 cm. If its length is 10 cm, find its breadth.
Answer:-Given:-[tex] \bullet [/tex] Perimeter (P) of a rectangle is 36 cm.
[tex] \bullet [/tex] Length (L) of a rectangle is 10 cm.
To Find:-Breadth (B) of a rectangle.
Solution:-We know,
P = 2(L + B)
So,
36 = 2(10 + B)
36 = 20 + 2B
36 - 20 = 2B
16 = 2B
B = 16/2 = 8 cm.
Breadth (B) of a rectangle is 8 cm. [Answer]At Ralphs Italian Ices, 145 sundaes were sold in June. Sales were up 23% in July. How many sundaes were sold in July?
Answers
Answer:
I Think 178
Step-by-step explanation:
I apologize for the messy photo but please help me with this, I’m really confused! Thank you so so so much.
Answers
1)+4
2)-4
3) 2
4) i don't know
5)
Answer: (-2)²=4
-2²=-4
square root of 4 is 2
1 over the square root of 8 is -2
1 aquare root of -8 is 2,-2
Step-by-step explanation:plug them into calculator