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Algebra
Question

\(P ( n ) \) , given below, is the price in dollar...

\(P ( n ) \) , 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) \( P ^ { - 1 } ( 8.8 ) = \square \) 

Answer

(a) Option B is correct 

 

(b) \(P^ { - 1} ( x) = \frac { 5x- 33} { 2} \)

 

(c) \(P^ { - 1} ( 8.8) = 5.5\)

Solution
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