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The problem asks to compute the composition of functions \( f(g(2)) \), where:

- \( f(x) = x^2 - 18 \)
- \( g(x) = 20 - x \)

We need to first evaluate \( g(2) \) and then substitute this result into \( f(x) \).

### Step-by-step solution:

1. **Find \( g(2) \):**
   \[
   g(2) = 20 - 2 = 18
   \]

2. **Substitute \( g(2) \) into \( f(x) \):**
   \[
   f(g(2)) = f(18)
   \]
   Now, use the function \( f(x) = x^2 - 18 \):
   \[
   f(18) = 18^2 - 18 = 324 - 18 = 306
   \]

Thus, \( f(g(2)) = 306 \).

Let me know if you have any questions, and here are a few related exercises:

1. What is \( g(f(2)) \)?
2. Find \( f(g(x)) \) for a general \( x \).
3. What is \( f(g(5)) \)?
4. If \( f(x) = x^2 + 10 \), what is \( f(g(3)) \)?
5. Find the inverse of \( f(x) \) and \( g(x) \), if they exist.

**Tip:** Always evaluate the inner function first in composition problems!

Let f(x) = x^2 - 18 and g(x) = 20 - x. Perform the composition or operation indicated. (fg)(2)

Learn how to solve the function composition problem f(g(2)) with f(x) = x^2 - 18 and g(x) = 20 - x. This problem focuses on key algebraic concepts such as function composition and quadratic equations. Suitable for students in Grades 9-10.

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