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.

f(x) = 7 + x, g(x) = x² - 2, h(x) = 3x. Find (h ∘ g ∘ f)(x).

Learn how to solve the composition of functions (h ∘ g ∘ f)(x) step by step, involving the functions f(x) = 7 + x, g(x) = x² - 2, and h(x) = 3x. This problem covers key concepts such as function composition and polynomial functions, suitable for students in Grades 10-12.

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