Chapter 1.8, Problem 62E

(a)

To determine

To find: The function $R$ in terms of $p$ that gives the cost of the hybrid car after receiving the rebate from the factory.

Answer to Problem 62E

The function is $R=p-2000$ .

Explanation of Solution

Given:

The dealership rebate on car is $\$2000$ and a discount of $10\%$ .

Calculation:

The cost of the car after the rebate from the factory is the difference of the cost of the car and the rebate that is,

  $R=p-2000$

(b)

To determine

To find: The function $S$ in terms of $p$ that gives the cost of the hybrid car after receiving the dealership discount.

Answer to Problem 62E

The function is $S=0.9p$ .

Explanation of Solution

Given:

The dealership discount is of $10\%$ .

Calculation:

The cost of the car after the discount is the difference of the car less than $10\%$ of the cost of the car that is,

  $\begin{array}{c}S=\left(1-0.1\right)p\\ =0.9p\end{array}$

(c)

To determine

To find: The interruption of the composite functions $\left(R\circ S\right)\left(p\right)$ and $\left(S\circ R\right)\left(p\right)$ .

Answer to Problem 62E

The function $\left(R\circ S\right)\left(p\right)=0.9p-2000$ is interpreted as the dealership discount applied to the price of the car before the factory discount.The function $\left(S\circ R\right)\left(p\right)=0.9\left(p-2000\right)$ is interrupted as the dealership discount that is applied to the price of the car after the factory discount is taken in to consideration.

Explanation of Solution

Given:

The give functions are $\left(R\circ S\right)\left(p\right)$ and $\left(S\circ R\right)\left(p\right)$ .

Calculation:

The composite function $\left(R\circ S\right)\left(p\right)$ is obtained by the substituting $S$ in $p$ for $R$ equation that given,

  $\left(R\circ S\right)\left(p\right)=0.9p-2000$

The above equation is interpreted as the dealership discount applied to the price of the car before the factory discount.

Consider the composite function that is found by plugging in $R$ in to $p$ for $S$ equation that gives,

  $\left(S\circ R\right)\left(p\right)=0.9\left(p-2000\right)$

The above equation is interrupted as the dealership discount that is applied to the price of the car after the factory discount is taken in to consideration.

(d)

To determine

To find: The value of $\left(R\circ S\right)\left(25795\right)$ and $\left(S\circ R\right)\left(25795\right)$ then determine which one of them lower cost of the hybrid car.

Answer to Problem 62E

The function $\left(R\circ S\right)\left(25795\right)=21215.5$ and the function $\left(S\circ R\right)\left(25795\right)=21415.5$ , thus the function $\left(R\circ S\right)\left(25795\right)$ cost lower for the hybrid car.

Explanation of Solution

Given:

The given functions are $\left(R\circ S\right)\left(25795\right)$ and $\left(S\circ R\right)\left(25795\right)=21415.5$ .

Calculation:

Consider the function,

  $\begin{array}{c}\left(R\circ S\right)\left(25795\right)=0.9\left(25795\right)-2000\\ =21215.5\end{array}$

Consider the function,

  $\begin{array}{c}\left(S\circ R\right)\left(25795\right)=\left(0.9\right)\left(25795-2000\right)\\ =21415.5\end{array}$

Thus, the function $\left(R\circ S\right)\left(25795\right)$ cost lower for the hybrid car.