To determine the difference in Cynthia's earnings between working as a camp counselor and as a lifeguard, we need to subtract the lifeguard earnings function from the camp counselor earnings function.
Here's the step-by-step process:
1. Define the earnings functions:
- As a camp counselor: \( f(x) = 10x + 50 \)
- As a lifeguard: \( g(x) = 15x + 25 \)
2. Determine the difference in earnings functions:
- We want to find \( (f - g)(x) \), which means we need to subtract \( g(x) \) from \( f(x) \).
3. Perform the subtraction:
- \( (f - g)(x) = f(x) - g(x) \)
- Substitute the given functions into the expression: \( f(x) - g(x) = (10x + 50) - (15x + 25) \)
4. Simplify the expression:
- Distribute the subtraction: \( (10x + 50) - (15x + 25) \)
- Combine like terms: \( 10x - 15x + 50 - 25 \)
- Simplify further: \( -5x + 25 \)
Therefore, the function representing the difference in Cynthia's earnings when working as a camp counselor instead of a lifeguard after \( x \) hours is:
[tex]\[ (f - g)(x) = -5x + 25 \][/tex]
From the given choices, the correct answer is:
[tex]\[ (f - g)(x) = -5x + 25 \][/tex]
