To find the inverse function [tex]\( n(a) \)[/tex], we need to start with the original function:
[tex]\[ a(n) = 3n - 20 \][/tex]
The goal is to express [tex]\( n \)[/tex] in terms of [tex]\( a \)[/tex]. Let's follow these steps:
1. Start by writing the original equation:
[tex]\[ a = 3n - 20 \][/tex]
2. To isolate [tex]\( n \)[/tex], first add 20 to both sides of the equation:
[tex]\[ a + 20 = 3n \][/tex]
3. Next, divide both sides by 3 to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{a + 20}{3} \][/tex]
Therefore, the inverse function [tex]\( n(a) \)[/tex] is:
[tex]\[ n(a) = \frac{a + 20}{3} \][/tex]
So, the correct answer is [tex]\( \boxed{A} \)[/tex].
