Choose the one alternative that best completes the statement or answers the question.
-To remodel a bathroom, a contractor charges $\$ 25$ per hour plus material costs, which amount to $\$ 3,775$. Therefore, the total cost to remodel the bathroom is given by $f ( x ) = 25 x + 3,775$ where $x$ is the number of hours the contractor works. Find a formula for $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 25 } - 151$; This computes the total cost if the contractor works $x$ hours.
B) $f ^ { - 1 } ( x ) = \frac { x } { 25 } - 151$; This computes the number of hours worked if the total cost is $x$ dollars.
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 25 } - 3,775$; This computes the total cost if the contractor works $x$ hours.
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 25 } - 3,775$; This computes the number of hours worked if the total cost is $x$ dollars.

Question

Quizplus · Accepted Answer

To find $f^{-1}(x)$, we solve for $x$ in terms of $y$: $y = 25x + 3775$. Solving for $x$, we get $x = \frac{y - 3775}{25}$, which simplifies to $x = \frac{y}{25} - 151$. Thus, $f^{-1}(x) = \frac{x}{25} - 151$, and it computes the number of hours worked if the total cost is $x$ dollars.

Choose the One Alternative That Best Completes the Statement or Answers