Solve the problem.
-A size 38 dress in Country C is size 11 in Country D. A function that converts dress sizes in Country C to those in Country $D$ is $f ( x ) = \frac { x } { 2 } - 8$. Find a formula for the inverse of the function described.
A) $f ^ { - 1 } ( x ) = 2 ( x - 8 )$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 2 \mathrm { x } + 8$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 8$
D) $f ^ { - 1 } ( x ) = 2 ( x + 8 )$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ in the original function $y = \frac{x}{2} - 8$, then solve for $y$. This gives $x = \frac{y}{2} - 8$, leading to $x + 8 = \frac{y}{2}$, and finally $y = 2(x + 8)$, which matches option D.

Solve the Problem DDD Is f(x)=x2−8f ( x ) = \frac { x } { 2 } - 8f(x)=2x​−8

Solve the Problem $D$ Is $f ( x ) = \frac { x } { 2 } - 8$