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Jawablah soal dengan nomor genap dan terjemahkan ke dalam bahasa Indonesia

Here are the solutions for the even-numbered problems (46) in both English and Indonesian:

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**46. \( H(x) = \sqrt[3]{\sqrt{x} - 1} \)**

We need to express \( H(x) \) in the form \( f \circ g \circ h \), which means we are looking for three functions such that:

\[
H(x) = (f \circ g \circ h)(x) = f(g(h(x)))
\]

Let's decompose the function step by step:

1. **Innermost function \( h(x) \):**
   The function \( \sqrt{x} \) (square root of \( x \)) appears first, so:
   \[
   h(x) = \sqrt{x} = x^{1/2}
   \]

2. **Middle function \( g(x) \):**
   The next operation is subtracting 1 from the result, so:
   \[
   g(x) = x - 1
   \]

3. **Outermost function \( f(x) \):**
   Finally, we take the cube root of the result, so:
   \[
   f(x) = \sqrt[3]{x} = x^{1/3}
   \]

Thus, \( H(x) = f(g(h(x))) \) is expressed as:
\[
f \circ g \circ h = \sqrt[3]{(\sqrt{x}) - 1}
\]

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### **Indonesian Translation:**

Kita perlu mengekspresikan \( H(x) \) dalam bentuk \( f \circ g \circ h \), yang berarti kita mencari tiga fungsi sehingga:

\[
H(x) = (f \circ g \circ h)(x) = f(g(h(x)))
\]

Mari kita uraikan fungsinya langkah demi langkah:

1. **Fungsi terdalam \( h(x) \):**
   Fungsi \( \sqrt{x} \) (akar kuadrat dari \( x \)) muncul pertama kali, jadi:
   \[
   h(x) = \sqrt{x} = x^{1/2}
   \]

2. **Fungsi tengah \( g(x) \):**
   Operasi selanjutnya adalah mengurangkan 1 dari hasilnya, jadi:
   \[
   g(x) = x - 1
   \]

3. **Fungsi terluar \( f(x) \):**
   Terakhir, kita mengambil akar kubik dari hasilnya, jadi:
   \[
   f(x) = \sqrt[3]{x} = x^{1/3}
   \]

Dengan demikian, \( H(x) = f(g(h(x))) \) dapat diekspresikan sebagai:
\[
f \circ g \circ h = \sqrt[3]{(\sqrt{x}) - 1}
\]

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Do you need further details or have any questions?  
Here are 5 questions that expand on this:

1. What are the steps for decomposing more complex functions into \( f \circ g \circ h \)?
2. Can you explain why we choose square root and cube root functions here?
3. How can we verify if the decomposition into \( f \circ g \circ h \) is correct?
4. What would happen if \( H(x) \) contained more complex nested functions?
5. Can we generalize this process to higher roots, like the fourth or fifth root?

**Tip:** When working with composite functions, always start by identifying the innermost operation and work your way outward.

Learn how to decompose composite functions like H(x) = (f ∘ g ∘ h)(x) with roots and powers, as demonstrated in the problem H(x) = ³√(√x - 1). This exercise is suitable for Grades 10-12 and focuses on function composition concepts, including roots and powers.

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