To find $(f + g)(x)$, we add the two functions $f(x)$ and $g(x)$ together:

Given:

$f(x) = 3x - 2$ $g(x) = 2x - 1$

Step 1: Add the two functions

$(f + g)(x) = f(x) + g(x) = (3x - 2) + (2x - 1)$

Step 2: Simplify the expression

$(f + g)(x) = 3x + 2x - 2 - 1 = 5x - 3$

So, $(f + g)(x) = 5x - 3$.

Step 3: Domain

Since both $f(x)$ and $g(x)$ are linear functions (polynomials of degree 1), their domains are all real numbers, $\mathbb{R}$. Adding them together does not restrict the domain.

Thus, the domain of $(f + g)(x)$ is all real numbers, written in interval notation as:

$\text{Domain} = (-\infty, \infty)$

Final Answer:

$(f + g)(x) = 5x - 3$ $\text{Domain} = (-\infty, \infty)$

Do you want more details on how the domain was determined or any other questions?

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Here are 5 related questions to further explore this topic:

1. What is $(f - g)(x)$ for the given functions?
2. What would $(f \cdot g)(x)$ look like?
3. Can you find the composite function $f(g(x))$?
4. How would you find the inverse of $f(x)$?
5. What is the slope of the line represented by $f(x)$?

Tip: When dealing with basic polynomial functions, the domain is often all real numbers unless you encounter divisions by zero or square roots of negative numbers.