andreyram25
Answered

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Question 3 of 25

If [tex]f(x) = 2x - 1[/tex] and [tex]g(x) = x^2 - 3x - 2[/tex], find [tex](f+g)(x)[/tex].

A. [tex](f+g)(x) = x^2 + 5x + 3[/tex]

B. [tex](f+g)(x) = x^2 - x - 3[/tex]

C. [tex](f+g)(x) = -x - 3[/tex]

D. [tex](f+g)(x) = x - 3[/tex]

Sagot :

GinnyAnswer
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]
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