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

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 $2065 .$