# The function f that shows the investigator’s fee in terms of x.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.7, Problem 81E

(a)

To determine

## The function f that shows the investigator’s fee in terms of x.

Expert Solution

The function f for the investigator’s fee is f(x)=500+80x

### Explanation of Solution

Given:

The investigator needs $500 retainer fee and$80perhour for his services.

Calculation:

Let the number of hour the investigator work be x,

The function to represent the retainer fee is $500 for investigator and$80perhour in terms of x is,

f(x)=retainerfee+$80perhourf(x)=500+80 For the x number of the hours, f(x)=500+80x Thus, the function for the x hours of work is f(x)=500+80x . (b) To determine ### The inverse of the function f(x)=500+80x . Expert Solution ## Answer to Problem 81E The inverse of the function f(x)=500+80x is f1(x)=180(x500) . ### Explanation of Solution Given: The function for the service of investigator for x number of hours is f(x)=500+80x . Calculation: Let the function be in terms of x and y, y=500+80x Solve for the value of x, y500=80xx=y50080 Further simplify the equation, x=180(y500) Interchange the value of x with y, y=180(x500) Thus, the value of inverse of the function is f1(x)=180(x500) . The inverse function shows the number of hours the investigator works. (c) To determine ### The value of f−1(1220) . Expert Solution ## Answer to Problem 81E The value of f1(1220) is 9. ### Explanation of Solution Given: The retainer fee for the investigator is$500 and the working hour of investigator is 1220.

Calculation:

The formula to calculate the working hours is,

f1(x)=180(x500) (1)

Where x is working hours.

Substitute 1220 for x in equation (1),

f1(x)=180(1220500)=180(720)=9

Thus the number of toppings on the pizza is 9. This shows that the investigator charges \$9 for 1220 number of hours.

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