Question

the average cost per person of attending an online class depends on the number of people attending. if 20 people attend, the web host charges $10 per person. if 26 people attend, the web host charges $6.25 per person. if 35 people attend, the web host charges $4 per person. which table represents the inverse of this function?

Explanation:

To determine the inverse function's table, we first analyze the original function. The original function \( f(x) \) maps the number of people \( x \) to the cost per person \( f(x) \). From the problem:

• When \( x = 20 \), \( f(20)=10 \)
• When \( x = 26 \), \( f(26)=6.25 \)
• When \( x = 35 \), \( f(35)=4 \)

The inverse function \( f^{-1}(y) \) maps the cost per person \( y \) back to the number of people \( x \). So we need to swap the \( x \) (input) and \( f(x) \) (output) values.

Step 1: Identify original function pairs

Original pairs: \( (20, 10) \), \( (26, 6.25) \), \( (35, 4) \)

Step 2: Swap to get inverse function pairs

After swapping, the inverse function pairs are: \( (10, 20) \), \( (6.25, 26) \), \( (4, 35) \)

Looking at the tables, the table where \( x \) (input of inverse) is 10, 6.25, 4 and \( f^{-1}(x) \) (output of inverse) is 20, 26, 35 matches these pairs.

Answer:

The table with \( x \) values 10, 6.25, 4 and \( f^{-1}(x) \) values 20, 26, 35 (the fourth table option as per the image layout, with \( x \) column: 10, 6.25, 4 and \( f^{-1}(x) \) column: 20, 26, 35).