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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.

Given: f(x) = x^3 + 2x - 3 and g(x) = 3x - 2, find 3g(0) - f(-1).

Learn how to solve the algebraic problem involving functions f(x) = x^3 + 2x - 3 and g(x) = 3x - 2. The problem focuses on finding 3g(0) - f(-1) using substitution. Suitable for students in Grades 9-10.

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