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To solve this, we need to find \( (f + g)(x) \), which is the sum of the functions \( f(x) \) and \( g(x) \).

The two functions are:

\[
f(x) = 3x^3 - 2x^2 + 4x - 5
\]
\[
g(x) = 6x - 7
\]

Now, add them together term by term:

\[
(f + g)(x) = (3x^3 - 2x^2 + 4x - 5) + (6x - 7)
\]

Combine like terms:

\[
(f + g)(x) = 3x^3 - 2x^2 + (4x + 6x) + (-5 - 7)
\]
\[
(f + g)(x) = 3x^3 - 2x^2 + 10x - 12
\]

Thus, the correct expression for \( (f + g)(x) \) is:

\[
(f + g)(x) = 3x^3 - 2x^2 + 10x - 12
\]

Now, looking at the multiple-choice options, the correct answer is **Option B**.

Would you like any additional details or have any further questions? 

Here are some related questions for further practice:
1. How would you subtract \( g(x) \) from \( f(x) \)?
2. What is \( f(x) + 2g(x) \)?
3. How do you find the derivative of \( f(x) + g(x) \)?
4. What is the integral of \( f(x) + g(x) \)?
5. How do you determine if \( f(x) + g(x) \) has any real roots?

**Tip:** When combining functions, always ensure you combine like terms correctly (terms with the same degree of \(x\)).

Find (f + g)(x) where f(x) = 3x^3 - 2x^2 + 4x - 5 and g(x) = 6x - 7.

Learn how to add the polynomial functions f(x) = 3x^3 - 2x^2 + 4x - 5 and g(x) = 6x - 7. This step-by-step solution teaches key algebra concepts like function addition and polynomial simplification. Suitable for students in Grades 9-12.

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