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!