Raffle tickets are being sold for a fundraiser. The function [tex]a(n)[/tex] relates the amount of money raised to the number of tickets sold, [tex]n[/tex].

It takes as input the number of tickets sold and returns as output the amount of money raised.
[tex]a(n) = 4n - 25[/tex]

Which equation represents the inverse function [tex]n(a)[/tex], which takes the money raised as input and returns the number of tickets sold as output?

A. [tex]n(a) = \frac{a}{4} - 25[/tex]

B. [tex]n(a) = \frac{a - 25}{4}[/tex]

C. [tex]n(a) = \frac{a + 25}{4}[/tex]

D. [tex]n(a) = \frac{a}{4} + 25[/tex]



Answer :

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.