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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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
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B2 = 24
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Substitute variables for the give numbers:
[tex]A=16(\frac{18+24}{2} )\\A = 336 in^2[/tex]
The 336 in is for one desk, and they want you to find 25 desks. So multiply 336 and 25.
[tex]x = 25(336)\\x = 8,400in^2[/tex]
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
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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]
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
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.
We want to round it to the nearest yard, then we need to look at the first digit after the decimal point. It is smaller than 5, then we round down, we get:
Radius = 26 yards.
what is the solution to 2(3m+4)=6(1-2m)
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c)m=-10
d.)m=1/5
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Answer:
The answer is in the picture below.
Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answer:
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Answers
Answer:
61.73 ft ^2
Step-by-step explanation:
area of rectangle
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area of circle
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question in screenshot
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Explanation: When you simply that’s the answer.
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.
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Step-by-step explanation:
Answer:
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Step-by-step explanation
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Step-by-step explanation:
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Step-by-step explanation:
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(NO LINKS)
Answers
Given:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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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 :-
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Hence the missing reasons in the proof are inscribed angles theorem.
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation: