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Income Tax In a certain country the tax on incomes less than or equal to €20,000 is 10%. For incomes that are more than €20,000 the tax is €2000 plus 20% of the amount over €20,000.
- (a) Find a function f that gives the income tax on an income x. Express f as a
piecewise defined function . - (b) Find f−1.What does f−1 represent?
- (c) How much income would require paying a tax of €10,000?
(a)
![Check Mark](/static/check-mark.png)
The function f that gives the income tax on income x.
Answer to Problem 87E
The function f for the income tax is
Explanation of Solution
Given:
The income tax on income less than €20000 is
Calculation:
Let the income tax be x,
Tax for the income €20000 is,
Tax for the income more than €20000 is,
From the equation (1) and (2),
Thus, the income tax for income x is
(b)
![Check Mark](/static/check-mark.png)
The inverse of the function
Answer to Problem 87E
The inverse of the function
Explanation of Solution
Given:
The income tax on income less than €20000 is
Calculation:
Solve for the income less than €20000,
Let the function be,
Solve for the value of x,
Interchange the value of x with y,
Thus, the value of inverse of the function is
Solve for the income more than €20000,
Let the function be,
Solve for the value of x,
Further solve the value,
Interchange the value of x with y,
Thus, the value of inverse of the function is
The inverse of the function
(c)
![Check Mark](/static/check-mark.png)
The income for the income tax €10000.
Answer to Problem 87E
The income for the income tax is 60000.
Explanation of Solution
Given:
The value of inverse of the function is
Calculation:
The formula to calculate the exchange of money is,
Substitute €10000 for x in equation (1),
Thus income for income tax is 60000.
Chapter 2 Solutions
EBK PRECALCULUS: MATHEMATICS FOR CALCUL
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