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You have two functions:  
\( f(x) = 5 - x \)  
\( g(x) = x^2 + 6x \)  

For part (a), you've already found that:  
\( (f - g)(x) = -x^2 - 7x + 5 \).

Now for part (b), we need to calculate \( (f - g)(3) \), which means substituting \( x = 3 \) into \( f(x) - g(x) \).

First, evaluate \( f(3) \) and \( g(3) \):
- \( f(3) = 5 - 3 = 2 \)
- \( g(3) = 3^2 + 6(3) = 9 + 18 = 27 \)

Now subtract:
\[
(f - g)(3) = f(3) - g(3) = 2 - 27 = -25
\]

So, \( (f - g)(3) = -25 \).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the expression change if \( f(x) \) were a quadratic function?
2. What happens if you switch the order and calculate \( g(x) - f(x) \)?
3. How would you solve \( (f - g)(x) = 0 \) for \( x \)?
4. What is the derivative of \( (f - g)(x) \)?
5. How does the composition \( (f \circ g)(x) \) differ from \( (f - g)(x) \)?

**Tip**: Always simplify the functions first before substituting values for better clarity!

For f(x) = 5 - x and g(x) = x^2 + 6x, find (f - g)(x) and (f - g)(3)

Learn how to subtract two functions, f(x) = 5 - x and g(x) = x^2 + 6x, and evaluate the result at x = 3. This problem explores function subtraction and evaluation, suitable for Grades 9-12.

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