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 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

Answer to Problem 88E

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

Answer to Problem 88E

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=fg

Expert Solution

Answer to Problem 88E

  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: H1 and what it means.

Expert Solution

Answer to Problem 88E

  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: H1(13000) and what it means.

Expert Solution

Answer to Problem 88E

  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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