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To solve for \( f(-2) \) and \( g(-6) \) using the given functions:

1. **Given Functions**:
   - \( f(x) = 2x^3 + 2 \)
   - \( g(x) = 2x - 1 \)

2. **Finding \( f(-2) \)**:
   Substitute \( x = -2 \) into \( f(x) \):
   \[
   f(-2) = 2(-2)^3 + 2
   \]
   Calculate \( (-2)^3 = -8 \), so:
   \[
   f(-2) = 2(-8) + 2 = -16 + 2 = -14
   \]
   Thus, \( f(-2) = -14 \).

3. **Finding \( g(-6) \)**:
   Substitute \( x = -6 \) into \( g(x) \):
   \[
   g(-6) = 2(-6) - 1
   \]
   Calculate \( 2(-6) = -12 \), so:
   \[
   g(-6) = -12 - 1 = -13
   \]
   Thus, \( g(-6) = -13 \).

### Final Answers:
- \( f(-2) = -14 \)
- \( g(-6) = -13 \)

Would you like additional details on any steps?

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Here are 5 related questions to deepen your understanding:
1. How would you calculate \( f(x) \) and \( g(x) \) for other values of \( x \)?
2. What would be the result of \( f(x) + g(x) \) for a given \( x \)?
3. How can we find the roots of \( f(x) = 0 \) or \( g(x) = 0 \)?
4. What is the degree and leading coefficient of \( f(x) \)?
5. How would you determine the inverse of \( g(x) \)?

**Tip**: To evaluate a function, substitute the given value for the variable and follow the order of operations carefully.

The functions f and g are defined as follows: f(x) = 2x^3 + 2 and g(x) = 2x - 1. Find f(-2) and g(-6). Simplify your answers as much as possible.

Learn how to evaluate the functions f(x) = 2x^3 + 2 and g(x) = 2x - 1 for specific values of x. This problem provides a detailed solution for finding f(-2) and g(-6), simplifying each result. Suitable for students in Grades 9-10.

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