Chapter ISG, Problem 4.7.5P

a.

To determine

To write a function

Answer to Problem 4.7.5P

  $f(x)=\frac{x}{4}$

Explanation of Solution

Given:

Profit is x dollars.

Calculation:

According to question,

Total profit= $x$ dollars.

Total friends=4

Hence, profit earned by each member is $\frac{x}{4}$ .

Function is $f(x)=\frac{x}{4}$ .

b.

To determine

To find inverse of the function

Answer to Problem 4.7.5P

  $f{(x)}^{-1}=$ $4x$

Explanation of Solution

Given information:

Function in above part.

Calculation:

If a function is mapping x to y, then inverse should map y back to x.

Let function be: $y=\frac{x}{4}$

Change the variables,

  $x=\frac{y}{4}$

Solving for y ,

  $y=4x$

Hence, inverse of function is $f{(x)}^{-1}=$ $4x$

c.

To determine

To describe inverse function in terms of problem.

Answer to Problem 4.7.5P

The answer is as follows.

Explanation of Solution

Given information:

Inverse of the function

In this problem, the inverse of the function can be described as the total profit earned by all of the friends where x is amount of profit earned by one person.

d.

To determine

To find best function to find how much each person received

Answer to Problem 4.7.5P

Each person received 37.5 dollars as profit.

Explanation of Solution

Given:

Profit earned= $250

Calculation:

According to question,

They put $100 in bank for equipment.

So, actual profit= $250-100$ =$150

Now, function to find how much each friend should get is $f(x)=\frac{x}{4}$ , where, $x$ is total profit.

Amount each friend should get is,

  $f(150)=\frac{150}{4}$

Solving,

  $f(150)=37.5$

Each friend should get $37.5 as profit.

e.

To determine

To find a function for how much profit should be made

Answer to Problem 4.7.5P

$400 is the profit

Explanation of Solution

Given:

Amount of profit earned by 1 partner=$75

Calculation:

The business should have $(profit+100) in order to get actual profit.

According to question,

Only profit want to be earned by each partner=$75

Hence, the best function to find the profit is $f{(x)}^{-1}=$

  $4x$ .

Now, by putting value, profit made is

  $f{(75)}^{-1}=4(75)$

  $f{(75)}^{-1}=300$

Total profit= ( $f{(75)}^{-1}$ +100)

  =300+100

  =$400

Hence, $400 is the profit to be made if everyone want to have $75 profit