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 $x$).