To find \((f + g)(x)\) given the functions \(f(x) = 2x - 1\) and \(g(x) = x^2 - 3x - 2\), we need to add these two functions together.
Here's the step-by-step process:
1. Write Down the Given Functions:
\( f(x) = 2x - 1 \)
\( g(x) = x^2 - 3x - 2 \)
2. Add the Functions Together:
[tex]\[
(f + g)(x) = f(x) + g(x)
\][/tex]
3. Substitute \( f(x) \) and \( g(x) \):
[tex]\[
(f + g)(x) = (2x - 1) + (x^2 - 3x - 2)
\][/tex]
4. Combine Like Terms:
[tex]\[
(f + g)(x) = x^2 + 2x - 3x - 1 - 2
\][/tex]
5. Simplify the Expression:
[tex]\[
(f + g)(x) = x^2 - x - 3
\][/tex]
Thus, the resulting function \((f+g)(x)\) is:
[tex]\[
(f + g)(x) = x^2 - x - 3
\][/tex]
So, the correct answer is:
B. [tex]\((f+g)(x) = x^2 - x - 3\)[/tex]
