Chapter MPS, Problem 7.3MPS

a.

To determine

To find which of $(f\circ g)(x)$ and $(g\circ f)(x)$ represent Adelina’s commission.

Answer to Problem 7.3MPS

  $(f\circ g)(x)$

Explanation of Solution

Given:

The given functions are-

  $f(x)=0.03x$ and $g(x)=x-5000$ . Adelina receives a $\$220$ weekly salary, plus a $3\%$ commission on sales over $\$5000$

Calculation:

Since her commission will be applied on the function $g(x)=x-5000$ by using the function $f(x)=0.03x$ , so her commission will be represented by $(f\circ g)(x)$ .

b.

To determine

To find Adelina’s commission on weekly sales of $\$11,675$ .

Answer to Problem 7.3MPS

  $\$200.25$ .

Explanation of Solution

Given:

The given functions are-

  $f(x)=0.03x$ and $g(x)=x-5000$ .

Calculation:

Adelina’s commission on weekly sales of $\$11,675$ is

  $\begin{array}{l}(f\circ g)(x)\\ =f(g(x))\\ =f(x-5000)\\ =0.03(x-5000)\\ =0.03x-150\\ =0.03\times 11,675-150\\ =350.25-150\\ =200.25\end{array}$

c.

To determine

To find the amount that Adelina will be paid for working a week in which her sales total $\$17,381$

Answer to Problem 7.3MPS

  $\$12752.43$ .

Explanation of Solution

Given:

The given functions are-

  $f(x)=0.03x$ and $g(x)=x-5000$ .

Calculation:

The total amount Adelina will be paid is equal to the her salary plus her commission

  $\begin{array}{l}g(x)=x-5000+(f\circ g)(x)\\ =x-5000+0.03x-150\\ =1.03\times 17,381-5150\\ =17,902.43-5150\\ =12752.43\end{array}$