Regarding the functions in this problem, it is found that:
a) The verbal description of the inverse is: Take the third root, subtract by 5 and divide by 3.
b) The formulas are:
c) The compositions result in x, hence they are inverses.
<h3>How to obtain the inverse function?</h3>
The original function is described as follows:
- Take the third power: (3x + 5)³.
Hence the function is:
y = (3x + 5)³.
To obtain the inverse functions, we exchange x and y and then isolate y, hence:
x = (3y + 5)³
![\sqrt[3]{x} = \sqrt[3]{(3y+5)^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%20%3D%20%5Csqrt%5B3%5D%7B%283y%2B5%29%5E3%7D)
![3y + 5 = \sqrt[3]{x}](https://tex.z-dn.net/?f=3y%20%2B%205%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
![3y = \sqrt[3]{x} - 5](https://tex.z-dn.net/?f=3y%20%3D%20%5Csqrt%5B3%5D%7Bx%7D%20-%205)
![y = \frac{\sqrt[3]{x} - 5}{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7Bx%7D%20-%205%7D%7B3%7D)
![f^{-1}(x) = \frac{\sqrt[3]{x} - 5}{3}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7Bx%7D%20-%205%7D%7B3%7D)
The verbal description of the inverse is:
- Take the third root. sqrt[3](x).
- Subtract by 5: sqrt[3](x) - 5.
The compositions are given as follows:
More can be learned about inverse functions at brainly.com/question/11735394
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1234xxx0 1`= 21 x3 2= 21x 3 3 =21x3 4= 21x 3 5=21x3 6=21x3 7=21x3 8=21x3 9=21 x3 irt will take him 588 secs
Answer:
B: 6 miles
Step-by-step explanation:
You divide 18 by 3 and get 6.
The answer is D, the yellow
Answer:
<u>L = 12 inches and W = 8 inches</u>
<u>Area = 96 in^2</u>
Step-by-step explanation:
Perimeter(P) = 2(width) + 2(length)
Let W = width and L = length
P = 2W + 2L
L = 2W - 4
Substitute: P = 2W + 2(2W - 4)
P = 6W - 8
P = 40 inches
40 = 6W - 8
6W = 48
W = 8
L = 2W - 4
L = 2(8) - 4
L = 12
<u>L = 12 inches and W = 8 inches</u>
<u>===============================</u>
Check to see if this works:
P = 2W + 2L
P = 2(12) + 2(8)
P = 24 + 16
P = 40 inches <u>YES</u>
<u>========</u>
Area = WxL
Area = (12)*(8)
<u>Area = 96 in^2</u>