\(P ( n ) \) , given below, is the price in dollars for \( n \) grams of vitamins.
\( P ( n ) = 0.4 n + 6.6 \)
Complete the following statements.
Let \( P ^ { - 1 } \) be the inverse function of \( P \) . Take \( x \) to be an output of the function \( P \) .
That is, \( x = P ( n ) \) and \( n = P ^ { - 1 } ( x ) \) .
(a) Which statement best describes \( P ^ { - 1 } ( x ) \) ?
The ratio of the price (in dollars) to the number of grams, \( x \) .
The amount of vitamins (in grams) for a price of \( x \) dollars.
The reciprocal of the price (in dollars) for \( x \) grams of vitamins.
The price (in dollars) for \( x \) grams of vitamins.
(b) \(P ^ { - 1 } ( x ) = \square \)
(c) \( P ^ { - 1 } ( 8.8 ) = \square \)