We are given three functions:

$f(x) = x^2 + 2, \quad g(x) = x - 1, \quad h(x) = 3 - 2x$

We are tasked with finding the composite function $(h \circ g \circ f)(x)$, which is written as:

$(h \circ g \circ f)(x) = h(g(f(x)))$

Step 1: Find $f(x)$

We are already given that:

$f(x) = x^2 + 2$

Step 2: Find $g(f(x))$

Now, substitute $f(x) = x^2 + 2$ into $g(x)$:

$g(f(x)) = g(x^2 + 2) = (x^2 + 2) - 1 = x^2 + 1$

Step 3: Find $h(g(f(x)))$

Next, substitute $g(f(x)) = x^2 + 1$ into $h(x)$:

$h(g(f(x))) = h(x^2 + 1) = 3 - 2(x^2 + 1) = 3 - 2x^2 - 2 = -2x^2 + 1$

Thus, the result of $(h \circ g \circ f)(x)$ is:

$h(g(f(x))) = -2x^2 + 1$

However, it seems none of the multiple-choice answers match directly, so there might be a typo in the problem or answers. The closest is answer C: -2x^2 - 4, but based on calculations, the correct expression is $-2x^2 + 1$.

Would you like further details or clarifications? Here are 5 questions to explore more:

1. What is the process of function composition, and how does it work?
2. Can function composition be commutative, or does the order always matter?
3. How would you approach solving if we had to reverse the process?
4. What other examples can we try for nested composite functions?
5. What happens if one function in the composition is not defined for certain values?

Tip: When solving function composition problems, always carefully apply each function step by step to avoid mistakes.