# A function f that models the purchase price of the car as a function of the sticker price 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 88E

a.

To determine

## To find: A function f that models the purchase price of the car as a function of the sticker price x .

Expert Solution

The function f that models the purchase price of the car as a function of the sticker price x when the discount price is 15% can be written as f(x)=85x100 .

### Explanation of Solution

Given information: The sticker price of the car is x . 15% Discount applies.

Concept used:

Steps for modeling with function:

1. To expresses the model in words

2. To choose the variables

3. Set up the model

4. Use the model

Calculation:

1. Expression of the model in words

We are to find the purchase price of the car as a function of the sticker price.

We know that, Purchase price=Sticar price × 100Discount100

2. Choosing of variable

Here the variable of is sticker price x .

3. Set up of model

The model is the function f that gives the purchase price of the car for any sticker price x .

Purchase price=Sticar price × 100Discount100

f(x)=x×10015100=85x100

The function f that models the purchase price of the car as a function of the sticker price x when the discount price is 15% can be written as f(x)=85x100 .

b.

To determine

### To find: A function g that models the purchase price of the car as a function of the sticker price x .

Expert Solution

The function g that models the purchase price of the car as a function of the sticker price x when $1000 rebate is$1000 be written as g(x)=x1000 .

### Explanation of Solution

Given information: The sticker price of the car is x . $1000 Rebate applies. Concept used: Steps for modeling with function: 1. To expresses the model in words 2. To choose the variables 3. Set up the model 4. Use the model Calculation: 1. Expression of the model in words We are to find the purchase price of the car as a function of the sticker price. We know that, Purchase price=Sticar price Rebate 2. Choosing of variable Here the variable of is sticker price x . 3. Set up of model The model is the function g that gives the purchase price of the car for any sticker price x . Purchase price=Sticar price Rebate g(x)=x1000 The function g that models the purchase price of the car as a function of the sticker price x when$1000 rebate is \$1000 be written as g(x)=x1000 .

c.

To determine

### To find: The formula H=f∘g

Expert Solution

H=85x85000100

H1(x) represents the sticker price of the car whose sell price x after discount and rebate.

### Explanation of Solution

Given information:

f(x)=85x100

g(x)=x1000

Formula used:

f(x)g(x)=f(g(x))

Calculation:

f(x)=85x100

g(x)=x1000

f(x)g(x)=f(g(x))=f(x1000)=85×(x1000)100=85x85000100

H=85x85000100

d.

To determine

### To find: H−1 and what it means.

Expert Solution

H1(x)=100x+8500085

H1(x) represents the sticker price of the car whose sell price x after discount and rebate.

### Explanation of Solution

Given information:

H=85x85000100

Formula used:

If, f(x)=y then   f1(y)=x

Calculation:

H(x)=85x85000100y=85x85000100100y=85x8500085x=100y+85000x=100y+8500085H1(y)=100y+8500085H1(x)=100x+8500085

H1(x) represents the sticker price of the car whose sell price x after discount and rebate.

e.

To determine

### To find: H−1(13000) and what it means.

Expert Solution

H1(13000)=16294.1176

H1(13000) it represents the sticker price of the car whose selling price is 13000 after rebate and discount.

### Explanation of Solution

Given information:

H1(x)=100x+8500085

Concept used:

To get the value of the function; we have to evaluate the right hand side of the function.

Calculation:

H1(13000)=100×13000+8500085=16294.1176

H1(13000) it represents the sticker price of the car whose selling price is 13000 after rebate and discount.

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