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We are given two functions, \( f(x) \) and \( g(x) \), and we need to find \( (f + g)(x) \), which means adding the two functions together.

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

### To find:
\[
(f + g)(x) = f(x) + g(x)
\]

### Step-by-step addition:
1. Start by adding the cubic terms: \( f(x) \) has a cubic term \( 7x^3 \), and \( g(x) \) has no cubic term.
   \[
   7x^3
   \]

2. Now, add the quadratic terms: \( f(x) \) has \( -3x^2 \), and \( g(x) \) has \( -2x^2 \).
   \[
   -3x^2 + (-2x^2) = -5x^2
   \]

3. Next, add the linear terms: \( f(x) \) has \( 4x \), and \( g(x) \) has \( 7x \).
   \[
   4x + 7x = 11x
   \]

4. Finally, add the constant terms: both functions have \( -6 \).
   \[
   -6 + (-6) = -12
   \]

### Therefore, the sum \( (f + g)(x) \) is:
\[
(f + g)(x) = 7x^3 - 5x^2 + 11x - 12
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. What is the difference \( (f - g)(x) \)?
2. How would you find \( (f \cdot g)(x) \), the product of \( f(x) \) and \( g(x) \)?
3. How do you find the derivative of \( (f + g)(x) \)?
4. What is the value of \( (f + g)(x) \) at a specific point, say \( x = 1 \)?
5. How would you graph \( (f + g)(x) \)?

**Tip:** When adding or subtracting polynomials, always combine like terms (terms with the same power of \( x \)).

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

Learn how to find (f + g)(x) by adding the polynomial functions f(x) = 7x^3 - 3x^2 + 4x - 6 and g(x) = -2x^2 + 7x - 6. This detailed solution covers the addition of polynomials and is suitable for students in Grades 9-12.

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