To find $(f+g)(8)$, we first need to add the two given functions $f(x)$ and $g(x)$, and then evaluate the result at $x = 8$.

Given:

• $f(x) = 5x^2 - 3x + 1$
• $g(x) = 4x^2 + 8x - 11$

Step 1: Add the functions:

$(f + g)(x) = f(x) + g(x)$ $(f + g)(x) = (5x^2 - 3x + 1) + (4x^2 + 8x - 11)$

Now, combine like terms: $(f + g)(x) = (5x^2 + 4x^2) + (-3x + 8x) + (1 - 11)$ $(f + g)(x) = 9x^2 + 5x - 10$

Step 2: Evaluate $(f + g)(x)$ at $x = 8$:

$(f + g)(8) = 9(8)^2 + 5(8) - 10$ $(f + g)(8) = 9(64) + 40 - 10$ $(f + g)(8) = 576 + 40 - 10$ $(f + g)(8) = 606$

Final Answer:

$(f + g)(8) = 606$

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:

1. What is the general process to combine two functions?
2. How would you find $f(x) \cdot g(x)$ for these functions?
3. How does the degree of the polynomial affect the graph of $f(x) + g(x)$?
4. How do we determine the zeros of $f(x) + g(x)$?
5. How do you find the inverse of a function?

Tip: Always check your algebraic simplifications carefully, especially when combining like terms!