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We are given two functions: \( f(t) = t^2 - t \) and \( h(x) = 3x + 8 \), and the task is to evaluate \( h(f(2)) \).

### Step-by-Step Solution:

1. **Evaluate \( f(2) \):**

   Using the given function \( f(t) = t^2 - t \), substitute \( t = 2 \):

   \[
   f(2) = 2^2 - 2 = 4 - 2 = 2
   \]

2. **Evaluate \( h(f(2)) \):**

   Now that we know \( f(2) = 2 \), substitute \( x = 2 \) into the function \( h(x) = 3x + 8 \):

   \[
   h(2) = 3(2) + 8 = 6 + 8 = 14
   \]

Thus, \( h(f(2)) = 14 \).

Would you like a detailed explanation of any step?

Here are five related questions to extend your understanding:
1. How would the answer change if \( f(t) \) were \( t^2 + t \) instead of \( t^2 - t \)?
2. Can you find \( h(f(-1)) \)?
3. What happens if the functions \( f \) and \( h \) are swapped, and we compute \( f(h(2)) \)?
4. What does it mean to compose functions like in this problem?
5. How would you graph \( h(f(x)) \)?

**Tip:** When evaluating compositions of functions, always work from the inside out!

Given f(t) = t^2 - t and h(x) = 3x + 8, evaluate h(f(2)).

This solution involves evaluating the function composition h(f(2)), where f(t) = t^2 - t and h(x) = 3x + 8. Learn the step-by-step approach for calculating h(f(t)) using substitution and function evaluation. Suitable for students in Grades 9-12.

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