The price \"P\" in dollars for \"n\" grams of vitamins is given below. P(n) = 0.

Question

The price "P" in dollars for "n" grams of vitamins is given below.
P(n) = 0.25n + 5.2
numy.valuating. and interpreting an inverse functic The price P in dollars for n grams of vitamins is given below. P(n)-0.25n+5.2 Complete the following statements. Let P1 be the inverse function of P. Take x to be an output of the function P. (a) Which statement best describes P1) O The ratio of the price (in dollars) to the number of grams, a. O The amount of vitamins (in grams) for a price ofas dollars O The reciprocal of the price (in dollars) for a grams of vitamins The price (in dollars) for x grams of vitamins. (b) 1 (x)- P Explanation Check

Explanation / Answer

Given the function P(n) = 0.25n + 5.2, price for n (grams)of vitamin

(a)

Say, x be an output for P(n) , where x will be the price of vitamin.

i.e.,

x = P(n) // take inverse on both sides,

P-1(x) = P-1(P(n))

=> P-1(x) = n

So, the P-1(x) will be tha amount of vitamins (in grams) for the price of x dollars.

Option 2 is the correct answer.

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(b) To find out the value of P-1, first replace P(n) with y

y = 0.25n + 5.2.

Now replace all y with n and all n with y

n = 0.25y + 5.2

Now solve for y;

0.25 y = n - 5.2

y = (n - 5.2) / 0.25

replace y with P-1(n)

P-1(n) = (n - 5.2) / 0.25

So,

P-1(x) = (x - 5.2) / 0.25

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(c)

we know

P-1(x) = (x - 5.2) / 0.25

so,

P-1(8.5) = (8.5 - 5.2) / 0.25

= 13.2

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