To find the inverse function [tex]\( N(a) \)[/tex] of the function [tex]\( A(n) = 3n - 20 \)[/tex], we need to express [tex]\( n \)[/tex] in terms of [tex]\( a \)[/tex].
Here are the steps we will take:
1. Start with the original function:
[tex]\[
A(n) = 3n - 20
\][/tex]
2. Replace [tex]\( A(n) \)[/tex] with [tex]\( a \)[/tex]: This is the first step in finding the inverse. By setting [tex]\( A(n) = a \)[/tex], we get:
[tex]\[
a = 3n - 20
\][/tex]
3. Solve for [tex]\( n \)[/tex]: We need to isolate [tex]\( n \)[/tex]. To do this, first add 20 to both sides of the equation:
[tex]\[
a + 20 = 3n
\][/tex]
4. Divide both sides by 3: To completely isolate [tex]\( n \)[/tex], divide both sides of the equation by 3:
[tex]\[
n = \frac{a + 20}{3}
\][/tex]
So the inverse function [tex]\( N(a) \)[/tex] is:
[tex]\[
N(a) = \frac{a + 20}{3}
\][/tex]
Considering the provided options, the correct answer is:
C. [tex]\( N(a) = \frac{a + 20}{3} \)[/tex]
