micah is running a sports trivia contest the entrance fee is $20 the winner will get $500 Micah keeps what is left over after paying the winner the function f(x)=20x-500 describes how much money Micah earns if x people enter the contest what does the inverse function f^-1(x) describe

Given: The entrance fee in contest = $20 and

Winner prize amount = $500.

Also what is left over after paying the winner the function :

f(x) = 20x-500, describes how much money Micah earns if x people enter the contest.

Solution: Let us find inverse function first.

Writing given function in terms of y.

y = 20x-500

Switching x and y, we get

x = 20y -500.

Now, solving it for y, we get

x +500 = 20y

[tex]\frac{x+500}{20} =y[/tex]

[tex]f^{-1}(x)=\frac{x+500}{20}[/tex].

Therefore, inverse function describes that the total number of people entered in the contest is the sum of winning amount and Micah's earning amount over the entrance fee of each contestant.