Find *f* ∘ *g* ∘ *h*.

*f*(*x*) = 

*x* − 1

,    *g*(*x*) = *x*2,    *h*(*x*) = *x*3 + 4

To find \( f \circ g \circ h \), we will follow the same steps as before:

1. **Find \( h(x) \)**: This is the innermost function.
   \[
   h(x) = x^3 + 4
   \]

2. **Find \( g(h(x)) \)**: Apply \( g(x) \) to \( h(x) \).
   \[
   g(h(x)) = g(x^3 + 4) = (x^3 + 4)^2
   \]

3. **Find \( f(g(h(x))) \)**: Finally, apply \( f(x) \) to \( g(h(x)) \).
   \[
   f(g(h(x))) = f((x^3 + 4)^2) = (x^3 + 4)^2 - 1
   \]

Thus, the composition \( f \circ g \circ h \) is given by:

\[
f \circ g \circ h(x) = (x^3 + 4)^2 - 1
\]

Would you like any further clarification on this process?

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Here are 5 related questions for further practice:

1. What is \( g \circ h(x) \) given \( g(x) = 2x \) and \( h(x) = x^2 + 5 \)?
2. Find \( f \circ g(x) \) if \( f(x) = x^2 + 3x \) and \( g(x) = \sqrt{x+1} \).
3. Calculate \( h(g(f(x))) \) given \( f(x) = x - 2 \), \( g(x) = x^2 + 1 \), and \( h(x) = 3x \).
4. Determine the simplified form of \( (x^3 + 4)^2 \).
5. What is the derivative of \( f \circ g \circ h(x) \) with respect to \( x \) given the functions in the problem?

**Tip:** For compositions of functions, carefully substitute each function into the next, starting from the innermost function. This approach helps avoid mistakes in complex expressions.

Discover how to find the composition f ∘ g ∘ h step-by-step. This problem involves functions f(x) = x - 1, g(x) = x^2, and h(x) = x^3 + 4. Learn the application of composition of functions and polynomial functions. Suitable for advanced high school students.

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