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!