The function that models the consumption of a certain medication over the years 2000-2010 is f(x)=115.21x+224.10 , where x is the number of years after 2000 and y is measured in grams per 100,000 people. Find the inverse of this function.
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 115.21 } - 224.10$
B) $f ^ { - 1 } ( x ) = \frac { 1 } { 115.21 x + 224.10 }$
C) $f ^ { - 1 } ( x ) = 115.21 ( x - 224.10 )$
D) $f ^ { - 1 } ( x ) = \frac { x - 224.10 } { 115.21 }$

Question

The function that models the consumption of a certain medication over the years  2000-2010  is  f(x)=115.21x+224.10 , where x  is the number of years after 2000 and  y  is measured in grams per 100,000 people. Find the inverse of this function.
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 115.21 } - 224.10$
B) $f ^ { - 1 } ( x ) = \frac { 1 } { 115.21 x + 224.10 }$
C) $f ^ { - 1 } ( x ) = 115.21 ( x - 224.10 )$
D) $f ^ { - 1 } ( x ) = \frac { x - 224.10 } { 115.21 }$

Quizplus · Accepted Answer

To find the inverse function, you swap $x$ and $y$ and solve for $y$. Starting with $y = 115.21x + 224.10$, swapping gives $x = 115.21y + 224.10$. Solving for $y$ gives $y = \frac{x - 224.10}{115.21}$, which matches choice D.

The Function That Models the Consumption of a Certain Medication f−1(x)=x115.21−224.10\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 115.21 } - 224.10f−1(x)=115.21x​−224.10

The Function That Models the Consumption of a Certain Medication $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 115.21 } - 224.10$