What is (f+g)(x)?f(x)=–5x+2g(x)=5xWrite your answer as a polynomial or a rational function in simplest form.

1. ### Break Down the Problem

We need to find the sum of two functions, $f(x)$ and $g(x)$. Given:

• $f(x) = -5x + 2$
• $g(x) = 5x$

To find $(f + g)(x)$, we will add these two functions together.

2. ### Relevant Concepts

The sum of two functions $f(x)$ and $g(x)$ is defined as: $(f + g)(x) = f(x) + g(x)$

3. ### Analysis and Detail

Let's perform the addition step by step: $(f + g)(x) = f(x) + g(x)$ Substituting the expressions for $f(x)$ and $g(x)$: $(f + g)(x) = (-5x + 2) + (5x)$

Now we will combine like terms:

1. Combine the $x$ terms: $-5x + 5x = 0$
2. The constant term remains as $2$.

Thus, $(f + g)(x) = 0 + 2 = 2$

4. ### Verify and Summarize

We have evaluated $(f + g)(x)$ step by step. The computation shows that all $x$ terms cancel out, leaving only a constant.

Final Answer

$(f + g)(x) = 2$