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We are tasked with finding \((f \circ h)(-3)\), which represents the composition of functions \(f(x)\) and \(h(x)\) evaluated at \(x = -3\).

Given:
- \(f(x) = 4x - 1\)
- \(h(x) = -x + 5\)

The composition of functions \((f \circ h)(x)\) means \(f(h(x))\). So, we first evaluate \(h(-3)\) and then substitute that result into \(f(x)\).

### Step 1: Find \(h(-3)\)
\[
h(x) = -x + 5
\]
\[
h(-3) = -(-3) + 5 = 3 + 5 = 8
\]

### Step 2: Find \(f(h(-3)) = f(8)\)
\[
f(x) = 4x - 1
\]
\[
f(8) = 4(8) - 1 = 32 - 1 = 31
\]

Thus, \((f \circ h)(-3) = 31\).

Would you like further clarification or details?

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Here are 5 related questions to consider:
1. What is the general process of function composition?
2. How do we reverse the roles and calculate \( (h \circ f)(-3) \)?
3. Can we perform composition with more than two functions?
4. What happens if \( f(x) \) and \( h(x) \) are inverse functions?
5. How do compositions affect domain and range?

**Tip**: Always calculate the inner function in compositions first, then substitute its result into the outer function.

Let f(x) = 4x - 1, h(x) = -x + 5. Find (f ∘ h)(-3).

Learn how to solve the function composition (f ∘ h)(-3) where f(x) = 4x - 1 and h(x) = -x + 5. This detailed step-by-step solution covers key algebraic concepts like function composition, suitable for Grades 9-11.

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