Chapter 9.9, Problem 39PPS

a.

To determine

To find $(f-g)(x)$ and $(g-f)(x)$ .

Answer to Problem 39PPS

  $(f-g)(x)=x^2+1$

  $(g-f)(x)=-(x^2+1)$

These are opposite of each other

Explanation of Solution

Given information:

  $f(x)=2x^2+x+3$

  $g(x)=x^2+x+2$

Calculation:

  $f(x)=2x^2+x+3$

  $g(x)=x^2+x+2$

  $(f-g)(x)=f(x)-g(x)$

Substituting value of f and g

  $(f-g)(x)=2x^2+x+3-[x^2+x+2]$

On solving

  $(f-g)(x)=x^2+1$

  $(g-f)(x)=g(x)-f(x)$

Substituting value of f and g

  $(g-f)(x)=[x^2+x+2]-[2x^2+x+3]$

On solving

  $(g-f)(x)=-(x^2+1)$

These are opposite of each other

b.

To determine

To graph $(f-g)(x)$ and $(g-f)(x)$ .

Answer to Problem 39PPS

  

Explanation of Solution

Given information:

  $(f-g)(x)=x^2+1$

  $(g-f)(x)=-(x^2+1)$

The graph of is given below

  $(f-g)(x)=x^2+1$

  $(g-f)(x)=-(x^2+1)$

The graph of above equations is given below

  

c.

To determine

To find how graph $(f-g)(x)$ and $(g-f)(x)$ are related.

Answer to Problem 39PPS

No solution

Explanation of Solution

Given information:

  $(f-g)(x)$ and $(g-f)(x)$

Calculation:

The graph of $(f-g)(x)$ and $(g-f)(x)$

given below

  

They never intersect as clear from graph.

Hence, no solution.

d.

To determine

To find the revenue from sale of jar .

Answer to Problem 39PPS

  $R(4)=552$

Explanation of Solution

Given information:

Vendor decided to charge $4.60 per jar

Revenue

  $R(x)=(4+0.15x)\times (160-10x)$

Calculation:

Let

  $f(x)=3x+2$

Let

  $g(x)=4-5x$

  $(f-g)(x)=[3x+2]+[4-5x]$

On solving,

  $(f-g)(x)=3x+2+4-5x$

  $=-2x+6$

  $(f-g)(x)=3x+2-[4-5x]$

On solving,

  $=8x-2$

It hold true sometimes and sometimes falls depend upon the functions.