We are given two functions:

• $f(x) = -3x - 1$
• $h(x) = -\frac{6}{x+1}$

We are tasked with finding $(f \circ h)(-3)$, which means we first need to evaluate $h(-3)$ and then substitute that result into $f(x)$.

Step 1: Evaluate $h(-3)$

$h(-3) = -\frac{6}{-3+1} = -\frac{6}{-2} = 3$

Step 2: Evaluate $f(h(-3)) = f(3)$

$f(3) = -3(3) - 1 = -9 - 1 = -10$

Thus, $(f \circ h)(-3) = -10$.

Would you like any further explanation?

Here are 5 related questions to expand on this concept:

1. What is the value of $(h \circ f)(-3)$?
2. How do you determine the domain of $f(x)$ and $h(x)$?
3. Can you find $(f \circ h)(0)$?
4. What happens when you compose $h$ with itself, i.e., $(h \circ h)(x)$?
5. How would you graph the composition $(f \circ h)(x)$?

Tip: When working with function compositions, always evaluate the inner function first before substituting its result into the outer function.