A Company's Profit $P$ For Producing $x$ Units Is Given By $P ( x ) = 47 x - 5736$

A company's profit $P$ for producing $x$ units is given by $P ( x ) = 47 x - 5736$ . Find the inverse function $P ^ { - 1 } ( x )$ and explain what it represents. Describe the domains of $P ( x )$ and $P ^ { - 1 } ( x )$ .

A) $P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }$ , $P ^ { - 1 } ( x )$ represents the number of units that must be sold to obtain the profit of $x$ .Domain of $P ( x ) : [ 0,10 )$ , Domain of $P ^ { - 1 } ( x ) : [ - 5736 , \infty )$
B) $P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }$ , $P ^ { - 1 } ( x )$ represents the number of units that must be sold to obtain the profit of $x$ .Domain of $P ( x ) : [ 0 , \infty )$ , Domain of $P ^ { - 1 } ( x ) : [ - 5736,5736 )$
C) $P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }$ , $P ^ { - 1 } ( x )$ represents the number of units that must be sold to obtain the profit of $x$ .Domain of $P ( x ) : [ 0 , \infty )$ , Domain of $P ^ { - 1 } ( x ) : [ - 5736 , \infty )$
D) $P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }$ , $P ^ { - 1 } ( x )$ represents the number of units that must be sold to obtain the profit of $x$ .Domain of $P ( x ) : [ 1 , \infty )$ , Domain of $P ^ { - 1 } ( x ) : [ - 5736 , \infty )$
E) $P ^ { - 1 } ( x ) = \frac { x + 5736 } { 47 }$ , $P ^ { - 1 } ( x )$ represents the number of units that must be sold to obtain the profit of $x$ .Domain of $P ( x ) : [ 0 , \infty )$ , Domain of $P ^ { - 1 } ( x ) : [ - 5736,47 )$