We are given two functions $g(x) = -6x + 1$ and $h(x) = -5x + 6$. We need to evaluate $g(-3)$, $h(-3)$, $g(h(x))$, and $g(h(-3))$.

1. Problem Description

We are given two functions $g(x) = -6x + 1$ and $h(x) = -5x + 6$. We need to evaluate $g(-3)$, $h(-3)$, $g(h(x))$, and $g(h(-3))$.

2. Solution Steps

First, we calculate $g(-3)$ by substituting $x = -3$ into the expression for $g(x)$:

$g(-3) = -6(-3) + 1 = 18 + 1 = 19$.

Next, we calculate $h(-3)$ by substituting $x = -3$ into the expression for $h(x)$:

$h(-3) = -5(-3) + 6 = 15 + 6 = 21$.

Now, we calculate $g(h(x))$ by substituting $h(x)$ into the expression for $g(x)$:

$g(h(x)) = g(-5x + 6) = -6(-5x + 6) + 1 = 30x - 36 + 1 = 30x - 35$.

Finally, we calculate $g(h(-3))$. We already know $h(-3) = 21$, so we need to calculate $g(21)$:

$g(h(-3)) = g(21) = -6(21) + 1 = -126 + 1 = -125$.

3. Final Answer

$g(-3) = 19$

$h(-3) = 21$

$g(h(x)) = 30x - 35$

$g(h(-3)) = -125$