We are given two functions:

• $f(x) = x^3 + 2x - 3$
• $g(x) = 3x - 2$

We need to find the value of $3g(0) - f(-1)$.

Step 1: Calculate $g(0)$

Using the function $g(x) = 3x - 2$, substitute $x = 0$: $g(0) = 3(0) - 2 = -2$ Now, multiply by 3: $3g(0) = 3(-2) = -6$

Step 2: Calculate $f(-1)$

Using the function $f(x) = x^3 + 2x - 3$, substitute $x = -1$: $f(-1) = (-1)^3 + 2(-1) - 3 = -1 - 2 - 3 = -6$

Step 3: Find $3g(0) - f(-1)$

Now, substitute the values: $3g(0) - f(-1) = -6 - (-6) = -6 + 6 = 0$

Thus, the answer is: $\boxed{0}$

Would you like further details on any step? Here are some related questions you can explore:

1. What is the derivative of $f(x)$ and $g(x)$?
2. How do you find the inverse of $f(x)$ and $g(x)$?
3. What would be $f(1) + g(1)$?
4. How would this process change if the functions were more complex, such as involving trigonometric terms?
5. What happens when you apply limits to these functions as $x \to \infty$?

Tip: Always substitute carefully when working with negative values to avoid sign errors.