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We are asked to find \((f + g)(x)\), given that:

- \( f(x) = -3x - 5 \)
- \( g(x) = 4x - 2 \)

To find \((f + g)(x)\), we simply add the two functions:

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

Substituting the given functions:

\[
(f + g)(x) = (-3x - 5) + (4x - 2)
\]

Now, simplify the expression:

\[
(f + g)(x) = -3x + 4x - 5 - 2
\]

\[
(f + g)(x) = x - 7
\]

Thus, \((f + g)(x) = x - 7\), which corresponds to option **B**.

Would you like more details or have any questions? Here are some related questions:

1. How do we perform function addition in general?
2. How would we handle subtracting two functions, like \((f - g)(x)\)?
3. What are some examples of function multiplication \((f \cdot g)(x)\)?
4. Can you find \((f \circ g)(x)\), the composition of functions for \(f(x)\) and \(g(x)\)?
5. What happens if \(f(x)\) or \(g(x)\) involves higher powers of \(x\)?

**Tip:** When adding or subtracting functions, always combine like terms (such as combining all terms involving \(x\) and constants separately).

If f(x) = -3x - 5 and g(x) = 4x - 2, find (f + g)(x).

Learn how to find the sum of two functions f(x) = -3x - 5 and g(x) = 4x - 2. Detailed step-by-step solution suitable for students in Grades 7-9.

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