Answer: ![f^{-1}(x) = \frac{\sqrt[3]{x^{2}}}{x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7Bx%5E%7B2%7D%7D%7D%7Bx%7D)
<u>Step-by-step explanation:</u>

Inverse is when you swap the x's and y's and then solve for "y":


![y = \frac{1}{\sqrt[3]{x}}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7Bx%7D%7D)
![y = \frac{1}{\sqrt[3]{x}}*(\frac{\sqrt[3]{x}}{\sqrt[3]{x}})^{2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7Bx%7D%7D%2A%28%5Cfrac%7B%5Csqrt%5B3%5D%7Bx%7D%7D%7B%5Csqrt%5B3%5D%7Bx%7D%7D%29%5E%7B2%7D)
![y = \frac{\sqrt[3]{x^{2}}}{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7Bx%5E%7B2%7D%7D%7D%7Bx%7D)
Answer:

And we can calculate the p value with the following probability taking in count the alternative hypothesis:

And for this case using a significance level of
we see that the p value is larger than the significance level so then we can conclude that we FAIL to reject the null hypothesis and we don't have enough evidence to conclude that the true proportion is less than 0.02
Step-by-step explanation:
For this case we want to test the following system of hypothesis:
Null hypothesis: 
Alternative hypothesis: 
The statistic for this case is given by:
(1)
And for this case we know that the statistic is given by:

And we can calculate the p value with the following probability taking in count the alternative hypothesis:

And for this case using a significance level of
we see that the p value is larger than the significance level so then we can conclude that we FAIL to reject the null hypothesis and we don't have enough evidence to conclude that the true proportion is less than 0.02
Let us first concentrate on the information’s
that are already given in the question. Based on those information’s the answer
to the question can be easily found.
Bill amount for Mr. Johnson before sales tax = $725
Percentage of sales tax taken = 6%
Then
Amount of sales tax = (6/100) * 725
= 4350/100 dollars
= 43.5 dollars
So the amount of sales tax that had to be given is $43.5.
<span>I hope the procedure for doing this
problem is clear to you.
</span>