The image shows two functions:

• $f(x) = 5x - 2$
• $g(x) = 3 - x^2$

You are asked to evaluate the following expressions:

1. $f(f(2))$
2. $g(g(3))$

(a) $f(f(2))$

First, calculate $f(2)$: $f(2) = 5(2) - 2 = 10 - 2 = 8$

Next, substitute $8$ into $f(x)$ again: $f(f(2)) = f(8) = 5(8) - 2 = 40 - 2 = 38$

So, $f(f(2)) = 38$.

(b) $g(g(3))$

First, calculate $g(3)$: $g(3) = 3 - 3^2 = 3 - 9 = -6$

Next, substitute $-6$ into $g(x)$: $g(g(3)) = g(-6) = 3 - (-6)^2 = 3 - 36 = -33$

So, $g(g(3)) = -33$.

Let me know if you'd like more details or if you have any questions!

Here are some related questions to expand the discussion:

1. What is the domain and range of the function $f(x)$?
2. How would you find the inverse of $g(x) = 3 - x^2$?
3. What happens if you compose $g(f(x))$ instead of $f(g(x))$?
4. How would you approach solving $f(f(x)) = 0$?
5. What is the effect of composing two quadratic functions?

Tip: When working with compositions of functions, it's important to solve them step by step and substitute carefully.