Let f(x) = 2x² - 4x + 1 and g(x) = -x² - 2x - 1 Find (f + g)(x)

To find \((f + g)(x)\), we simply add the two functions \(f(x)\) and \(g(x)\):

\[
f(x) = 2x^2 - 4x + 1
\]
\[
g(x) = -x^2 - 2x - 1
\]

Now, adding the corresponding terms from both functions:

\[
(f + g)(x) = (2x^2 - 4x + 1) + (-x^2 - 2x - 1)
\]

Simplifying each term:

- \(2x^2 + (-x^2) = x^2\)
- \(-4x + (-2x) = -6x\)
- \(1 + (-1) = 0\)

Thus, the result is:

\[
(f + g)(x) = x^2 - 6x
\]

### Final Answer:
\[
(f + g)(x) = x^2 - 6x
\]

Would you like further details or have any other questions?

### Related Questions:
1. How do you subtract functions, such as \( (f - g)(x) \)?
2. What happens when you multiply \(f(x)\) and \(g(x)\)?
3. How do you find the domain of \( (f + g)(x) \)?
4. Can you find the derivative of \( f(x) \) and \( g(x) \)?
5. How do you find the zeros of \( (f + g)(x) \)?

### Tip:
When adding or subtracting functions, always combine like terms (terms with the same powers of \(x\)).

Learn how to add two quadratic functions, f(x) = 2x² - 4x + 1 and g(x) = -x² - 2x - 1, to find (f + g)(x). This problem covers algebraic concepts such as combining like terms and simplifying quadratic functions. Suitable for students in Grades 8-10.

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