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The function [tex]c(n)[/tex] below relates the number of bushels of apples picked at a pick-your-own orchard to the final cost for the apples.

It takes as input the number of bushels of apples picked after paying an entry fee to an orchard, and it returns as output the cost of the apples (in dollars).

[tex]\[ c(n) = 15n + 30 \][/tex]

Which equation below represents the inverse function [tex]n(c)[/tex], which takes the cost of the apples as input and returns the number of bushels picked as output?

A. [tex]\[ n(c) = \frac{c-30}{15} \][/tex]

B. [tex]\[ n(c) = \frac{c-15}{30} \][/tex]

C. [tex]\[ n(c) = \frac{c+15}{30} \][/tex]

D. [tex]\[ n(c) = \frac{c+30}{15} \][/tex]



Answer :

GinnyAnswer
To find the inverse of the function \( c(n) = 15n + 30 \), we need to:

1. Swap \( c \) and \( n \) in the equation.
2. Solve for \( n \) in terms of \( c \).

Here is the step-by-step process:

1. Start with the original equation:
[tex]\[ c(n) = 15n + 30 \][/tex]

2. Swap \( c \) and \( n \):
[tex]\[ c = 15n + 30 \][/tex]

3. Isolate \( n \) by first subtracting 30 from both sides:
[tex]\[ c - 30 = 15n \][/tex]

4. Divide both sides by 15 to solve for \( n \):
[tex]\[ n = \frac{c - 30}{15} \][/tex]

So, the inverse function \( n(c) \) is:
[tex]\[ n(c) = \frac{c - 30}{15} \][/tex]

Therefore, the correct equation is:

A. [tex]\( n(c) = \frac{c - 30}{15} \)[/tex]

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