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]
