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?

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.