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 $x$).