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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To equal the step 2, we would have to determine that 20 was our new denominator and multiply the first fraction by 5, the second by 4 and the 2 by 20.
multiplied by sides of the equation by 20
Answer:
D=10t+5
Step-by-step explanation:
D(0)=10*0+5=5
D(1)=10*1+5=15
D(2)=10*2+5=25
D(3)=10*3+5=35
D(4)=10*4+5=45
Answer:
2000 + .05x >= 2200
Step-by-step explanation:
2000 is how much she already has
.05 is 5% of sales
x is the unknown amount of sales
2200 is how much she needs
The rate is just 5% increase.
Answer:
<h2>x = 3.1</h2>
Step-by-step explanation:
<h3>
</h3>
<u>To solve first take logarithm to both sides</u>
That's
<h3>
</h3><h3 /><h3>
</h3>
But
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</h3>
So we have
<u>Write 1200 as a number with the factor 100</u>
That's
1200 = 100 × 12
So we have
<h3>
</h3>
<u>Using the rules of logarithms</u>
That's
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</h3>
Rewrite the expression
That's
<h3>
</h3><h3 /><h3>
</h3><h3>
</h3><h3>
</h3><h3 /><h3>
</h3>
x = 3.079
So we have the final answer as
<h3>x = 3.1 to one decimal place</h3>
Hope this helps you
