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GRAPHS AND FUNCTIONSFinding, evaluating, and interpreting an inverse function for a giv...P(n), given below, is the price P in dollars for n grams of vitamins.P (n) 0.25n 5.2Complete the following statements.1be the inverse function of P.Let PTake x to be an output of the function P1(x)?(a) Which statement best describes P?The price (in dollars) for x grams of vitamins.The ratio of the price (in dollars) to the number of grams, xThe reciprocal of the price (in dollars) for x grams of vitamins.The amount of vitamins (in grams) for a price of x dollars.- 1(x) =(b) Р-1P(8.5)(c)X

Question

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GRAPHS AND FUNCTIONS
Finding, evaluating, and interpreting an inverse function for a giv...
P(n), given below, is the price P in dollars for n grams of vitamins.
P (n) 0.25n 5.2
Complete the following statements.
1
be the inverse function of P.
Let P
Take x to be an output of the function P
1
(x)?
(a) Which statement best describes P
?
The price (in dollars) for x grams of vitamins.
The ratio of the price (in dollars) to the number of grams, x
The reciprocal of the price (in dollars) for x grams of vitamins.
The amount of vitamins (in grams) for a price of x dollars.
- 1
(x) =
(b) Р
-1
P
(8.5)
(c)
X
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GRAPHS AND FUNCTIONS Finding, evaluating, and interpreting an inverse function for a giv... P(n), given below, is the price P in dollars for n grams of vitamins. P (n) 0.25n 5.2 Complete the following statements. 1 be the inverse function of P. Let P Take x to be an output of the function P 1 (x)? (a) Which statement best describes P ? The price (in dollars) for x grams of vitamins. The ratio of the price (in dollars) to the number of grams, x The reciprocal of the price (in dollars) for x grams of vitamins. The amount of vitamins (in grams) for a price of x dollars. - 1 (x) = (b) Р -1 P (8.5) (c) X

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Step 1

Given:

The price function P(n) is defined as P(n) =0.25n+5.2,where n is the number of
grams of vitamins
Consider P
to be the inverse function ofP and take x to be an output ofP.
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The price function P(n) is defined as P(n) =0.25n+5.2,where n is the number of grams of vitamins Consider P to be the inverse function ofP and take x to be an output ofP.

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Step 2

a]

The inverse function P1 (x) describes the number of grams of vitamins bought for x
dollars
Hence, the fourth statement "The amount of vitamins for a piece ofx dollars" is correct
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The inverse function P1 (x) describes the number of grams of vitamins bought for x dollars Hence, the fourth statement "The amount of vitamins for a piece ofx dollars" is correct

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Step 3

b]

...
Obtain the value of P(x)as follows.
P(n) 0.25n5.2
0.25n P-5.2
0.25n
Р-5.2
0.25
0.25
п34(Р-5.2)
That is, n 4P -20.8
=
As the price is x dollars and P1 (x) is the amount of vitamins, the obtained equation
becomes P(x)= 4x - 20.8
Therefore, P x)=4x-20.8
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Obtain the value of P(x)as follows. P(n) 0.25n5.2 0.25n P-5.2 0.25n Р-5.2 0.25 0.25 п34(Р-5.2) That is, n 4P -20.8 = As the price is x dollars and P1 (x) is the amount of vitamins, the obtained equation becomes P(x)= 4x - 20.8 Therefore, P x)=4x-20.8

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Calculus

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