The Supply Function for a Product Is $p ( x ) = \frac { 1 } { 3 } x ^ { 2 } + 50$

Multiple Choice

The supply function for a product is $p ( x ) = \frac { 1 } { 3 } x ^ { 2 } + 50$ where x is the number of thousands of units a manufacturer will supply if the price is p(x) dollars. Find the inverse of this function.

A) $p ^ { - 1 } ( x ) = \frac { 1 } { 3 } \sqrt { x } + 50$
B) $\mathrm { p } ^ { - 1 } ( \mathrm { x } ) = 3 \sqrt { \mathrm { x } } - 50$
C) $\mathrm { p } ^ { - 1 } ( \mathrm { x } ) = 3 \sqrt { ( \mathrm { x } - 50 ) }$
D) $p ^ { - 1 } ( x ) = \sqrt { 3 ( x - 50 ) }$