Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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]


Sagot :

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]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.