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.
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Y = {13,57}
Which of the following is the set XnY?
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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:
Given: Circle O; ZA intercepts BC; ZD intercepts BC Two statements are missing reasons. What reason can be used to justify both statements 2 and 3? Prove: ZA ZD Statements Reasons D 1. given A 1. circle O; ZA intercepts BC, ZD intercepts BC 2. m ZA= (MBC ) 3.m4D = 1mBC) (MBC 12.1? B 3.? 4. mZA=mZD 4. substitution property 5. ZASZD 5. definition of congruent angles O inscribed angles theorem
Answers
Answer:
A. Inscribed angle theorem
Step-by-step explanation:
The missing reasons in the proof are inscribed angles theorem.
What is an arc in a circle?In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.
Given that, a circle, with arcs AD and BC, we need to find the reason in the proof,
The reasons are inscribed angles theorem.
Inscribed angles theorem :-
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.
Hence the missing reasons in the proof are inscribed angles theorem.
Learn more about arcs, click;
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What is the approximate value of 12−−√ ?
3.5
2
6
4.5
Answers
Find the lengths of the legs.
(NO LINKS)
Answers
Given:
The figure of a right angle triangle with hypotenuse 10 and two angles [tex]45^\circ, 90^\circ[/tex]
To find:
The lengths of the legs.
Solution:
Two angles are given. By using the angle sum property, the third angle is:
Third angle = [tex]180^\circ-45^\circ- 90^\circ[/tex]
= [tex]45^\circ[/tex]
Base angles are equal it means the given triangle is an isosceles right triangle. So, the lengths of both legs are equal.
Let x be the lengths of both legs. Then by using Pythagoras theorem, we get
[tex]Hypotenuse^2=leg_1^2+leg_2^2[/tex]
[tex](10)^2=x^2+x^2[/tex]
[tex]100=2x^2[/tex]
[tex]\dfrac{100}{2}=x^2[/tex]
[tex]50=x^2[/tex]
Taking square root on both sides, we get
[tex]\pm \sqrt{50}=x[/tex]
[tex]\pm 5\sqrt{2}=x[/tex]
[tex]\pm 5\sqrt{2}=x[/tex]
The side length cannot be negative. So, the only value of x is [tex]5\sqrt{2}[/tex].
Therefore, the length of the both legs is [tex]5\sqrt{2}[/tex] units.
Help!!!!!! Which function is best represented by this graph
Answers
Answer:j
Step-by-step explanation:
Answer:
J
Step-by-step explanation:
in the graph, the vector terminating at A represents the complex number z. the vector terminating at B represents the product of z and -2. which graph correctly represents the product?y
Answers
Answer: The first one in the picture.
Step-by-step explanation: I got this right on Edmentum.
*There’s a picture below
question in screenshot
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Explanation: When you simply that’s the answer.
Need help on this question thanks
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Answer:median
Step-by-step explanation: because median is used to be in the middle so those are numbers that would be in the middle, and if you add them up it would contain a high amount of number but if you subtract half you get your answer, and your Welcom!
What is the total surface area of the triangular prism shown?
Answers
Answer:
24 2/5ft
Step-by-step explanation:
add all the sides together.
4ft x 2
3ft x 2
10 2/5 x 1
=
24 2/5
1) Determine the area of the shaded region.
14 ft
8 ft
Answers
Answer:
61.73 ft ^2
Step-by-step explanation:
area of rectangle
14x8 = 112
area of circle
π(4)(4) = 50.27
subtract
112-50.27 = 61.73
Substituting the equation x = 4y – 12 into the equation -2y = x – 6 will produce the equation _________.
Answers
-2y = 4y-12 -6
y = x + 45
What is the y-intercept of the relationship?
A. 45
B. x + 45
C. x
D. y - 45
Answers
Answer:
D
Step-by-step explanation:
Find the mean of 9, 2, 2, 1, 1 graphically.
Answers
15/5= 3
Kim is evaluating the expression 20 - 3p + 1 when p=4. Which expression can Kim use to evaluate the expression correctly?
Answers
Answer:
20-3(4)+1
Step-by-step explanation:
Find the amount due if $200 is borrowed for 10 months at an APR of 16% simple interest
Amount =?
Answers
Answer
$266.66
Step-by-step explanation:
We have here ,
Principal = $200 Rate = 16% Time = 10 months = 10/12 yrs.We can use the formula of SI to calculate the SI . After adding it to principal we will get the amount .
⇒ SI = P × R × T / 100
⇒ SI = $ 200 × 16 × 10 / 12 × 100
⇒ SI = $ 26.66
Now Calculate amount as ,
⇒ A = SI + P
⇒ A = $ 200 + $ 26.66
⇒ A = $ 226.66
CAN SOMEONE PLZZZ HELP ME? THIS IS DUE IN LIKE 5 MINUTES
Answers
Answer:
I think E im not sure which other one.
Step-by-step explanation:
Answer:
A and E
Step-by-step explanation:
hope this helps and hope you get a good score on your assignment/test/quiz
Simplify 1 1/8 x 4 +2 5/6 x 3
Answers
Answer:
bro just search it on mathaway or calculator soup
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
Please help!!! Solve for the m
Answers
Answer:
36°
Step-by-step explanation:
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Gretta is 1 1/2 meters tall. Which of the following is equivalent to 1 1/2 meters? A 150 millimeters B 1.500 millimeters C 100 millimeters D 1,000 millimeters
Answers
Answer:
1500 millimeters is your answer
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Answers
Answer:
What do you mean? If you are talking about the Community not always answering Questions well that means your they don't know the right Answer
the Mods are Annoying and very skeptic of the Guidelines of Brainly.
At the beginning of the month, Sarah had 600 in her bank account. Within the month she made two deposits of and She also made three withdrawals 100, , and 20. How much was in her account at the end of the month?
Answers
Answer:
At the end of the month she has $578
Step-by-step explanation:
Given
[tex]Start\ balance = 600[/tex]
[tex]Deposits=50; 100; 48[/tex]
[tex]Withdrawal: 100; 20; 100[/tex]
Required
The balance at month end
Deposits simply means adding cash to the account and it has a very simple interest. So, we add .
While Withdrawal taking money out of the account. So, we subtract.
So, we have:
[tex]Month\ end = Start\ balance + Deposits + Withdrawal[/tex]
[tex]Month\ end = 600 + [50 + 100 + 48] - [100 + 20 + 100])[/tex]
[tex]Month\ end = 600 + 198 - 220])[/tex]
[tex]Month\ end = 578[/tex]
Hence, at the end of the month she has $578
A sprinkler rotates 360° to water a circular region. If the total area watered is approximately 2,200yd2, determine the radius of the region (the radius is length of the stream of water). Round the answer to the nearest yard.
Answers
Answer:
Radius = 26 yards.
Step-by-step explanation:
The complete rotation of the sprinkler makes a circle of radius R (R is the length of the stream of water).
Remember that the area of a circle of radius R is:
A = pi*R^2
where pi = 3.14
In this case, we know that the area is equal to 2,200 yd^2
Then:
A = 2,200 yd^2 = 3.14*R^2
Solving this equation we can find the value R.
(2,200 yd^2)/3.14 = R^2
√( (2,200 yd^2)/3.14) = R = 26.47 yards.
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Answers
Answer:
6,912 i think that's the answer I'm not sure though
Step-by-step explanation:
Answer:
[tex]8,400in^2[/tex]
Step-by-step explanation:
Area of Trapezoid: [tex]A=h(\frac{b1+b2}{2} )[/tex]
Given: B1, B2 and h
B1 = 18 in
B2 = 24
h = 16 in
Substitute variables for the give numbers:
[tex]A=16(\frac{18+24}{2} )\\A = 336 in^2[/tex]
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3 1/7 x 10 answer plz
Answers
Answer:
31.43
Step-by-step explanation:
3 1/7 = 3.14285714285
3 1/7 x 10 = 31.4285714286 which is about 31.43
Answer:
31 [tex]\frac{3}{7}[/tex]
Step-by-step explanation:
[tex]\frac{22}{7}[/tex]×[tex]\frac{10}{1}[/tex]
[tex]\frac{220}{7}[/tex]
31 [tex]\frac{3}{7}[/tex]
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Answers
Answer:
4
Step-by-step explanation:
what is the solution to 2(3m+4)=6(1-2m)
a) m=2
b) m=-2
c)m=-10
d.)m=1/5
Answers
Answer:
The answer is in the picture below.
Step-by-step explanation:
The weight of 8 science books is 28 pounds. What is the weight of 11 science books?
The weight of 11 science books is
pounds.
Answers
Answer:
11 books = 33 Pounds
Step-by-step explanation:
24 divided by 8 = 3 pounds per book.
3 x 11 = 33 pounds
Hope this helps
Answer:
38.5
Step-by-step explanation:
28÷8=3.5
3.5×11=38.5
what is the domain of this exponential function , y=7^x
Answers
Answer: hope this helps
Step-by-step explanation:
Answer:
Hope this helped!!!
Step-by-step explanation:
WHAT THE HECK IS THAT SHAPE PLEASE HELP IM SLOW
Answers
Answer: It looks like a Trapezoid
Step-by-step explanation:
Answer:
trapezoid
Step-by-step explanation
there are two lines across from each toher that are parallel, but the other two lines aren't , so this has to be a trapezoid. there are also no right angles
Which One Doesn't Belong (WODB)
Indicate which multiplication problem you believe does NOT belong in the group.
Explain Why!
Answers
Answer:
I think A does not belong to the multiplication problems, because A's outcome is 2 digit while the others are 1 digit.
Step-by-step explanation: