Question

The function c(n) 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).
c(n) = 10n + 20
Which equation below represents the inverse function n(c), which takes the cost of the apples as input and returns the number of bushels picked as output?
On (c) = ct-20
On (c) = *+10
On (c) = c-20
10
On (c) = 9-10
20

Answer 1

To find the inverse function \( n(c) \) from the function \( c(n) = 10n + 20 \), we start by expressing \( c \) in terms of \( n \):

1. Set \( c(n) = c \):
\[
c = 10n + 20
\]

2. Solve for \( n \):
\[
c - 20 = 10n
\]
\[
n = \frac{c - 20}{10}
\]

Thus, the inverse function \( n(c) \) is:
\[
n(c) = \frac{c - 20}{10}
\]

Now we can analyze the given options to find the equation that represents this inverse function:

- \( n(c) = \frac{c-20}{10} \)

This expression matches what we've derived.

Hence, the correct choice is:
\[
n(c) = \frac{c - 20}{10}
\]