For the Functions F(x) and G(x), Evaluate the Indicated Function $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } )$

question 9

Multiple Choice

For the functions f(x) and g(x) , evaluate the indicated function.
-The amount of money, in billions of dollars, spent on health care that was covered by insurance in a certain country in a particular year can be approximated by the function f(x) = x2 + 14x + 279,
Where x represents the number of years after 2005. The amount of money, in billions of dollars,
Spent on health care that was paid out of pocket in a certain country in a particular year can be
Approximated by the function g(x) = 9x + 149, where again x represents the number of years after
2005. (i) Find $( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } )$ . Explain, in your own words, what this function represents.
(ii) Find ( $\mathrm { f } - \mathrm { g } ) ( 60 )$ . Explain, in your own words, what this number represents.

• A) (i) \(( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 23 \mathrm { x } - 428\); this is the difference between health-care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, \(x\) years after \(2005 .\)
• (ii) 1792 ; health-care costs covered by insurance will be \(\$ 1,792,000,000,000\) less than health-care costs that are paid out of pocket in \(2065 .\)
• B) (i) \(( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 130\); this is the difference between health-care costs covered by insurance and health-care costs that are paid out of pocket, in billions of dollars, \(x\) years after \(2005 .\)
• (ii) 4030 ; health-care costs covered by insurance will be \(\$ 4,030,000,000,000\) higher than health-care costs that are paid out of pocket in \(2065 .\)
• C) (i) \(( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 130\); this is the difference between health-care costs that are paid out of pocket and those that are covered by insurance, in billions of dollars, \(x\) years after 2005 .
• (ii) 4030 ; health-care costs covered by insurance will be \(\$ 4,030,000,000,000\) less than health-care costs that are paid out of pocket in \(2065 .\)
• D) (i) \(( \mathrm { f } - \mathrm { g } ) ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 23 \mathrm { x } - 428\); this is the difference between health-care costs covered by insurance and health-care costs that are paid out of pocket, in billions of dollars, \(x\) years after \(2005 .\)
• (ii) 1792 ; health-care costs covered by insurance will be \(\$ 1,792,000,000,000\) higher than health-care costs that are paid out of pocket in \(2065 .\)

---

Definitions:

Early English Colonists

The first settlers from England who established colonies in the New World, mainly during the 16th and 17th centuries.

Indians

Refers to the people from India, a country in South Asia recognized for its diverse culture, languages, and traditions, or to Indigenous peoples of the Americas.

Virginia Company

An English joint-stock company chartered in 1606 with the purpose of establishing colonial settlements in North America, leading to the foundation of Jamestown, Virginia.

Land Ownership

The legal right or title to control and use a specific plot of land, recognized and protected by law.