To solve for [tex]\((f - g)(100)\)[/tex], we need to understand the meaning of the functions and perform the calculations step-by-step.
1. Understanding the Functions:
- [tex]\( f(x) = 4x + 5000 \)[/tex], which represents the amount of money made from selling [tex]\( x \)[/tex] televisions.
- [tex]\( g(x) = 20x - 500 \)[/tex], which represents the cost of producing [tex]\( x \)[/tex] televisions.
2. Calculating [tex]\( f(100) \)[/tex]:
[tex]\[
f(100) = 4 \cdot 100 + 5000 = 400 + 5000 = 5400
\][/tex]
So, the revenue from selling 100 televisions is [tex]$5400.
3. Calculating \( g(100) \):
\[
g(100) = 20 \cdot 100 - 500 = 2000 - 500 = 1500
\]
Thus, the cost of producing 100 televisions is $[/tex]1500.
4. Calculating [tex]\( (f - g)(100) \)[/tex]:
[tex]\[
(f - g)(100) = f(100) - g(100) = 5400 - 1500 = 3900
\][/tex]
Therefore, the difference between the revenue and the cost, which represents the profit from selling 100 televisions, is [tex]$3900.
Given these detailed steps, the accurate interpretation is:
\( (f - g)(100) = 3900 \), and this represents the profit made from selling 100 televisions.
So, the correct answer is:
\(\boxed{\text{b. } \$[/tex] 3,900 \text{ is the profit made from 100 televisions.}}\)
