To solve $(h \circ g \circ f)(x)$, which is the composition of the functions $h(x)$, $g(x)$, and $f(x)$, we'll work step by step.

1. Step 1: Find $f(x)$: $f(x) = 7 + x$

2. Step 2: Plug $f(x)$ into $g(x)$: We need to substitute $f(x)$ into $g(x)$. So, $g(f(x)) = g(7 + x)$. $g(7 + x) = (7 + x)^2 - 2$ Expand the square: $(7 + x)^2 = 49 + 14x + x^2$ Now subtract 2: $g(7 + x) = 49 + 14x + x^2 - 2 = 47 + 14x + x^2$

3. Step 3: Plug $g(f(x))$ into $h(x)$: Now substitute $g(f(x))$ into $h(x)$. So, $h(g(f(x))) = h(47 + 14x + x^2)$. $h(47 + 14x + x^2) = 3(47 + 14x + x^2)$ Distribute the 3: $h(47 + 14x + x^2) = 141 + 42x + 3x^2$

Thus, $(h \circ g \circ f)(x) = 141 + 42x + 3x^2$.

Would you like more details, or do you have any questions?

Here are 5 related questions for you:

1. How would you find $(g \circ h)(x)$?
2. What is the derivative of $(h \circ g \circ f)(x)$?
3. Can you find $(f \circ g \circ h)(x)$?
4. How do the graphs of these composed functions look?
5. What happens when you compose functions in a different order?

Tip: When composing functions, always substitute the innermost function first and work outward.