find (f+g)(8) if f(x)=5x2-3x+1 and g(x)=4x2+8x-11

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!

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

Learn how to find (f+g)(8) where f(x)=5x^2-3x+1 and g(x)=4x^2+8x-11. This problem involves adding polynomial functions and evaluating at a specific value. Suitable for students in Grades 9-10.

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