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.