(a)
In the function P(n) = 0.4n +5.7, P(n) is price of n grams of vitamins. So for the function x = P(n); x is price of n grams of vitamins.
The inverse of function determine amount of the vitamins for the known price of x dollars. So answer is,
The amount of vitamins (in grams) for a price of x dollars.
(b)
Let P(n) = x, So
Replace n by x and x by n in the given equation.
Simplify the equation for x.
So inverse of function is after interchange of variables,
(c)
Substitute 8.3 for x in the inverse equation to obtain the valur of P^-1(8.3).
So answer is 6.5.