Let ​f(x)=− 3 and ​g(x)=x2−x. Find and simplify the expression.
​(f+​g)(3​)

To find \((f+g)(3)\), we start by understanding that the expression \((f+g)(x)\) represents the sum of the functions \(f(x)\) and \(g(x)\):

\[
(f+g)(x) = f(x) + g(x)
\]

Given:
- \(f(x) = -3\)
- \(g(x) = x^2 - x\)

### Step 1: Substitute and Simplify \(f(3)\) and \(g(3)\)

1. **Find \(f(3)\):**
   \[
   f(3) = -3
   \]

2. **Find \(g(3)\):**
   \[
   g(3) = 3^2 - 3 = 9 - 3 = 6
   \]

### Step 2: Substitute into \((f+g)(3)\)

Now, we substitute the values we found for \(f(3)\) and \(g(3)\):
\[
(f+g)(3) = f(3) + g(3) = -3 + 6 = 3
\]

### Answer
\[
(f+g)(3) = 3
\]

Would you like further explanation on any steps?

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Here are some related questions:
1. What is the domain of \(f(x) + g(x)\) if \(f(x) = -3\) and \(g(x) = x^2 - x\)?
2. How would the result change if \(f(x) = 3\) instead of \(-3\)?
3. Can we rewrite \((f \cdot g)(x)\) using \(f(x) = -3\) and \(g(x) = x^2 - x\)?
4. How do we interpret \((f - g)(x)\) in terms of \(f(x)\) and \(g(x)\)?
5. What if we calculated \((f/g)(3)\) with the given functions?

**Tip:** When finding the sum of functions at a specific value, evaluate each function separately at that value before adding them.

Let f(x) = -3 and g(x) = x^2 - x. Find and simplify the expression (f+g)(3).

Learn how to find and simplify the expression (f+g)(3) using given functions f(x) = -3 and g(x) = x^2 - x. This step-by-step solution covers function operations, substitution, and simplification concepts. Suitable for students in Grades 8-10.

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