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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.7, Problem 87E

(a)

To determine

The function *f* that gives the income tax on income *x*.

Expert Solution

The function *f* for the income tax is

**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)

To determine

The inverse of the function

Expert Solution

The inverse of the function

**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)

To determine

The income for the income tax €10000.

Expert Solution

The income for the income tax is 60000.

**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.