Question
You belong to a gym where the base membership is \( \$ 36 \) per month and each group fitness class you take costs an additional \( \$ 2.75 \) per class. Write a function in \( x \) that represents the total amount you spend on your gym membership in a month. Be sure to indicate any domain restrictions. Answer 2 Points
Ask by Pierce Carrillo. in the United States
Jan 23,2025
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Tutor-Verified Answer
Answer
The total monthly cost \( f(x) \) is \( 36 + 2.75x \), where \( x \) is the number of group fitness classes. \( x \) must be a whole number and at least zero.
Solution
Let \( f(x) \) represent the total monthly cost, where \( x \) is the number of group fitness classes taken.
\[
f(x) = 36 + 2.75x
\]
**Domain Restrictions:**
- \( x \) must be a whole number (i.e., \( x \) is an integer) because you can't attend a fraction of a class.
- \( x \geq 0 \) since you can't take a negative number of classes.
**Summary:**
\[
f(x) = 36 + 2.75x \quad \text{for} \quad x \in \mathbb{Z}, \ x \geq 0
\]
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Simplify this solution Mind Expander
The total amount spent on your gym membership in a month can be represented by the function \( T(x) = 36 + 2.75x \), where \( T(x) \) is the total cost and \( x \) is the number of group fitness classes attended. This function calculates your base membership fee plus the cost of the classes you take. As for the domain restrictions, since you cannot attend a negative number of classes, \( x \) must be a non-negative integer. Therefore, the domain of \( x \) is \( x \geq 0 \).
