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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!

Let f(x) = -4x - 1, h(x) = -x + 3. Find (f o h)(6).

Learn how to solve a function composition problem with detailed steps for f(x) = -4x - 1 and h(x) = -x + 3. Explore how to evaluate the composition of functions and apply algebraic principles. Suitable for high school students.

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