To solve for $f(3)$ and $g(-4)$ using the given functions:

$f(x) = -4x - 1 \quad \text{and} \quad g(x) = 2x^3 + 6$

Step 1: Find $f(3)$

Substitute $x = 3$ into $f(x)$:

$f(3) = -4(3) - 1$

$f(3) = -12 - 1$

$f(3) = -13$

Step 2: Find $g(-4)$

Substitute $x = -4$ into $g(x)$:

$g(-4) = 2(-4)^3 + 6$

First, calculate $(-4)^3$:

$(-4)^3 = -64$

Now substitute:

$g(-4) = 2(-64) + 6$

$g(-4) = -128 + 6$

$g(-4) = -122$

Final Answers:

1. $f(3) = -13$
2. $g(-4) = -122$

Would you like me to explain any step further?

Related Questions:

1. What is $f(-2)$ for the same function $f(x)$?
2. What is $g(2)$ for the same function $g(x)$?
3. How can you determine if $f(x)$ is linear?
4. Find $g(0)$ and explain its significance.
5. If $h(x) = f(x) + g(x)$, what is $h(3)$?

Tip: When evaluating functions, always substitute the given value carefully and simplify step by step.