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We are given the functions \( f(x) = 3x - 1 \) and \( h(x) = -x + 1 \), and asked to find \( (h \circ f)(4) \), which means we need to find \( h(f(4)) \).

### Step-by-step solution:
1. **Find \( f(4) \)**:
   \[
   f(x) = 3x - 1
   \]
   Substitute \( x = 4 \):
   \[
   f(4) = 3(4) - 1 = 12 - 1 = 11
   \]

2. **Find \( h(f(4)) = h(11) \)**:
   \[
   h(x) = -x + 1
   \]
   Substitute \( x = 11 \):
   \[
   h(11) = -(11) + 1 = -11 + 1 = -10
   \]

Thus, \( (h \circ f)(4) = -10 \).

Would you like further explanation or details on any step?

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Here are 5 related questions:
1. What is \( (f \circ h)(4) \)?
2. How do you find the composition of two functions in general?
3. What is the result of \( (h \circ f)(x) \) for a general \( x \)?
4. If \( f(x) = 2x + 3 \) and \( h(x) = x^2 - 1 \), what is \( (h \circ f)(2) \)?
5. Can you explain the graphical interpretation of \( h(f(x)) \)?

**Tip**: Always check your composition step-by-step, starting with the innermost function first!

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

Learn how to solve a function composition problem: (h o f)(4) where f(x) = 3x - 1 and h(x) = -x + 1. This step-by-step guide walks you through finding the value of h(f(4)) using algebraic methods. Suitable for Grades 9-11.

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