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

question 40

Multiple Choice

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 \(P ^ { - 1 } ( x ) : [ - 5736,47 )\)