The given function is $f(x) = x^2 + x + 6$. We need to compute the following:

Part A: $f(-3) + f(5)$

1. Calculate $f(-3)$:

   $f(-3) = (-3)^2 + (-3) + 6 = 9 - 3 + 6 = 12$

2. Calculate $f(5)$:

   $f(5) = (5)^2 + 5 + 6 = 25 + 5 + 6 = 36$

3. Now add $f(-3)$ and $f(5)$:

   $f(-3) + f(5) = 12 + 36 = 48$

Part B: $f(-3) - f(5)$

1. We already know $f(-3) = 12$ and $f(5) = 36$.

2. Now subtract $f(5)$ from $f(-3)$:

   $f(-3) - f(5) = 12 - 36 = -24$

Final Answers:

• A) $f(-3) + f(5) = 48$
• B) $f(-3) - f(5) = -24$

Would you like more details or have any questions?

Related Questions:

1. How would the result change if the function were $f(x) = x^2 + 2x + 6$?
2. What is the derivative of $f(x) = x^2 + x + 6$?
3. Can you find $f(0) + f(2)$ for the same function?
4. What is the graph of $f(x) = x^2 + x + 6$ like?
5. How does completing the square affect the function $f(x) = x^2 + x + 6$?

Tip:

When working with functions, always carefully substitute the values and simplify step by step to avoid mistakes.