Let's break down the given problem step-by-step.

You are asked to use the functions $f(x) = 5x - 2$ and $g(x) = 3 - x^2$ to evaluate the following expressions:

(a) $(f \circ g)(-2)$

This is the composition of functions, meaning you first evaluate $g(-2)$ and then substitute that result into $f(x)$.

1. Evaluate $g(-2)$: $g(-2) = 3 - (-2)^2 = 3 - 4 = -1$

2. Now, substitute $g(-2) = -1$ into $f(x)$: $f(-1) = 5(-1) - 2 = -5 - 2 = -7$

Thus, $(f \circ g)(-2) = -7$.

(b) $(g \circ f)(-2)$

This is also a composition of functions, but this time you first evaluate $f(-2)$ and then substitute that result into $g(x)$.

1. Evaluate $f(-2)$: $f(-2) = 5(-2) - 2 = -10 - 2 = -12$

2. Now, substitute $f(-2) = -12$ into $g(x)$: $g(-12) = 3 - (-12)^2 = 3 - 144 = -141$

Thus, $(g \circ f)(-2) = -141$.

Let me know if you need any further details or if something was unclear.

Here are five related questions to expand on this:

1. What is the general formula for the composition of two functions?
2. How would you compute $(f \circ g)(x)$ for any value of $x$?
3. Can you describe how function composition differs from regular function evaluation?
4. What are the domains of the composed functions $(f \circ g)(x)$ and $(g \circ f)(x)$?
5. How would the result change if different values for $x$ were chosen?

Tip: When working with function compositions, always evaluate the innermost function first!