A raffle has a 50$ gift card to a miniature golf course as a prize. It cost 4 & per game. Write a function that represents the amount of money left after x games. write the inverse of the function from part a, which function would you use to find out how many gamer were played when 10$ was left on the card?

To write a function that represents the amount of money left on the $50 gift card after playing a certain number of games at $4 per game, we can follow these steps:

1. Define the variable for the number of games played.

2. Calculate the cost of playing those games.

3. Subtract that cost from the initial amount on the gift card.

Let $ g $ represent the number of games played. Each game costs $4, so the total cost for $ g $ games is $ 4g $. The initial amount on the gift card is $50.

The function $ f(g) $ representing the amount of money left on the gift card after playing $ g $ games is given by:

\[ f(g) = 50 - 4g \]

Where:

- $ f(g) $ is the amount of money left on the gift card after playing $ g $ games.

- 50 is the initial amount of money on the gift card.

- 4g is the total cost of playing $ g $ games at $4 per game.

Example Calculations

- If no games are played ($ g = 0 $):

\[ f(0) = 50 - 4 \cdot 0 = 50 \]

- If 5 games are played ($ g = 5 $):

\[ f(5) = 50 - 4 \cdot 5 = 50 - 20 = 30 \]

- If 10 games are played ($ g = 10 $):

\[ f(10) = 50 - 4 \cdot 10 = 50 - 40 = 10 \]

Summary

The function $ f(g) = 50 - 4g $ effectively calculates the remaining balance on the gift card after a certain number of games have been played.