amarieon999
Answered

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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].

The function [tex]\( a(n) = 3n - 20 \)[/tex] takes the number of tickets sold as input and returns the amount of money raised as output.

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]\( n(a) = \frac{a + 20}{3} \)[/tex]
B. [tex]\( n(a) = \frac{a}{3} + 20 \)[/tex]
C. [tex]\( n(a) = \frac{a - 20}{3} \)[/tex]
D. [tex]\( n(a) = \frac{a}{3} - 20 \)[/tex]

Sagot :

GinnyAnswer
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].
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