Question: 4. [3 pts.] Find $f \circ g \circ h$ when $f(x) = \frac{1}{x}$, $g(x) = x^2$, $h(x) = x^3 + 2$.
1. **State the problem:** We need to find the composition $f \circ g \circ h$, which means $f(g(h(x)))$.
2. **Recall the functions:**
- $f(x) = \frac{1}{x}$
- $g(x) = x^2$
- $h(x) = x^3 + 2$
3. **Step 1: Compute $h(x)$:**
$$h(x) = x^3 + 2$$
4. **Step 2: Compute $g(h(x))$:**
Substitute $h(x)$ into $g$:
$$g(h(x)) = (h(x))^2 = (x^3 + 2)^2$$
5. **Step 3: Compute $f(g(h(x)))$:**
Substitute $g(h(x))$ into $f$:
$$f(g(h(x))) = \frac{1}{g(h(x))} = \frac{1}{(x^3 + 2)^2}$$
6. **Final answer:**
$$f \circ g \circ h (x) = \frac{1}{(x^3 + 2)^2}$$
This is the composition of the three functions.