To find the inverse function [tex]\( n(a) \)[/tex] of the given function [tex]\( a(n) = 4n - 25 \)[/tex], we want to express [tex]\( n \)[/tex] in terms of [tex]\( a \)[/tex].
Step-by-step, the process is as follows:
1. Start with the given function:
[tex]\[
a(n) = 4n - 25
\][/tex]
2. To find the inverse, we need to solve for [tex]\( n \)[/tex] in terms of [tex]\( a \)[/tex]. So, we set [tex]\( a(n) = a \)[/tex] (where [tex]\( a \)[/tex] is the output or the amount of money raised):
[tex]\[
a = 4n - 25
\][/tex]
3. Next, isolate [tex]\( n \)[/tex]. Begin by adding 25 to both sides of the equation to move the constant term to the other side:
[tex]\[
a + 25 = 4n
\][/tex]
4. Now, solve for [tex]\( n \)[/tex] by dividing both sides by 4:
[tex]\[
n = \frac{a + 25}{4}
\][/tex]
This represents the inverse function [tex]\( n(a) \)[/tex], which takes the amount of money raised [tex]\( a \)[/tex] as input and returns the number of tickets sold [tex]\( n \)[/tex].
Thus, the equation representing the inverse function is:
[tex]\[
n(a) = \frac{a + 25}{4}
\][/tex]
So the correct answer is:
[tex]\[
\boxed{n(a) = \frac{a + 25}{4}}
\][/tex]
Option C is the correct choice.
