BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 81E

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 f1(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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