The problem is asking to find $(f \circ h)(6)$, which is the composition of the functions $f(x)$ and $h(x)$ evaluated at $x = 6$.

We are given:

• $f(x) = -4x - 1$
• $h(x) = -x + 3$

Step 1: Find $h(6)$

Substitute $x = 6$ into the equation for $h(x)$:

$h(6) = -(6) + 3 = -6 + 3 = -3$

Step 2: Use $h(6)$ as input for $f(x)$

Now that we have $h(6) = -3$, substitute this value into the equation for $f(x)$:

$f(-3) = -4(-3) - 1 = 12 - 1 = 11$

Final Answer:

$(f \circ h)(6) = 11$

Would you like any further details or have any questions?

Here are 5 related questions to explore further:

1. What is the composition of two functions, and how is it defined?
2. How do you compute $(f \circ h)(x)$ for any arbitrary $x$?
3. What happens if you change the order of composition, i.e., $(h \circ f)(6)$?
4. How would the result change if one of the functions had a different form?
5. What are some real-world applications of function composition?

Tip: When dealing with composition, always start by evaluating the innermost function first!