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 returns as output the cost of the apples (in dollars).
c(n)=20n+15
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?
A) n(c)=c+20/15
B) n(c)=c-15/20
C) n(c)=c+15/20
D) n(c)=c-20/15

Answer 1

C(n) = 20n + 15

y = 20n + 15
20n = y - 15
n = (y - 15)/20


B.)
N(c) = (c-15)/20


(:

Answer 2

Follow these steps in order to find the inverse of a linear function:

1. Replace function notation ( c(n) for our problem ) with y

2. Exchange x and y

3. Solve for y

4. Replace appropriate variables

Let's find the inverse of
`c(n)=20n+15`.

`y=20n+15\\x=20y+15\\x-15=20y\\y=(x-15)/(20)`

This is the inverse. The last part requires us to replace variables appropriately. So instead of y, we should put n(c) and instead of x we should put c.

We have
`n(c)=(c-15)/(20)`

Answer choice B is right.

ANSWER: B