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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) = 20n + 15[/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-15}{20}[/tex]
B. [tex]n(c) = \frac{c-20}{15}[/tex]
C. [tex]n(c) = \frac{c+15}{20}[/tex]
D. [tex]n(c) = \frac{c+20}{15}[/tex]

Sagot :

GinnyAnsweridn
To find the inverse function [tex]\( n(c) \)[/tex] of the given function [tex]\( o(n) = 20n + 15 \)[/tex], we need to express [tex]\( n \)[/tex] in terms of [tex]\( c \)[/tex].

Given:
[tex]\[ o(n) = 20n + 15 \][/tex]

First, set [tex]\( o(n) = c \)[/tex] to represent the cost in terms of the number of bushels:
[tex]\[ c = 20n + 15 \][/tex]

Next, solve this equation for [tex]\( n \)[/tex]:

1. Subtract 15 from both sides:
[tex]\[ c - 15 = 20n \][/tex]

2. Divide both sides by 20 to isolate [tex]\( n \)[/tex]:
[tex]\[ n = \frac{c - 15}{20} \][/tex]

Thus, the inverse function [tex]\( n(c) \)[/tex] is:
[tex]\[ n(c) = \frac{c - 15}{20} \][/tex]

Therefore, the correct answer is:

A. [tex]\( n(c) = \frac{c - 15}{20} \)[/tex]
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