To find \((f + q)(x)\), we need to add the two functions \(f(x)\) and \(q(x)\).

Given:
\[
f(x) = f(x) - 2x + 1
\]
\[
q(x) = -x^2 + 2x + 2
\]

We assume that the expression for \(f(x)\) provided, \(f(x) - 2x + 1\), actually defines \(f(x)\) as a function, so we simplify the first part:

1. Simplify \(f(x) - 2x + 1\) to obtain the actual expression for \(f(x)\).
   
\[
f(x) = f(x) - 2x + 1
\]

This expression can be interpreted in different ways depending on the correct definition of \(f(x)\), so we'll assume a scenario where:

If \(f(x) = 2x - 1\) was intended, then this term would cancel to:

\[
f(x) - (2x - 1) = 0 
\]

But since you’ve not defined \(f(x)\), I assume you mean to work with \(f(x) = f(x)\). So let's add it straight:

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

If you're defining \(f(x)\) implicitly in a format, I can adjust, but here's a result as a function:

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

Thus, the expression could simplify directly for specific forms of \(f(x)\) - typically in the cases when you'd confirm exactly what \(f(x)\) stands for.

Would you like to provide further context or require another step? Here are some steps that would help:

---

1. Can we assume any specific values for \(f(x)\)?
2. Do you mean to subtract \(2x\) from the original \(f(x)\)?
3. Do you want to assume \(f(x)\) as a polynomial?
4. Could we work with a specific example for \(f(x)\)?
5. Does the function involve transformations or values you're testing?

---

**Tip:** Try to specify all terms in the function explicitly so the calculations go smoothly.


f(x) - 2x + 1, q(x) = -x^2 + 2x + 2; find (f + q)(x)

This page provides a step-by-step solution for adding two polynomial functions: f(x) = 2x - 1 and q(x) = -x^2 + 2x + 2. Learn the process of function addition, crucial algebraic concepts, and explore polynomial properties. Ideal for students in Grades 9-11.

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