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The problem asks for the value of \( (f \circ g)(x) \), which is the composition of functions \( f(x) \) and \( g(x) \).

We are given:
- \( f(x) = x^5 + 1 \)
- \( g(x) = \sqrt[5]{x - 1} \)

The composition \( (f \circ g)(x) \) means we substitute \( g(x) \) into \( f(x) \):
\[
(f \circ g)(x) = f(g(x))
\]

### Step-by-Step Calculation:
1. First, compute \( g(x) \):
   \[
   g(x) = \sqrt[5]{x - 1}
   \]

2. Now substitute \( g(x) \) into \( f(x) \):
   \[
   f(g(x)) = f\left(\sqrt[5]{x - 1}\right)
   \]

3. Use the definition of \( f(x) = x^5 + 1 \):
   \[
   f\left(\sqrt[5]{x - 1}\right) = \left(\sqrt[5]{x - 1}\right)^5 + 1
   \]

4. Simplify:
   \[
   \left(\sqrt[5]{x - 1}\right)^5 = x - 1
   \]
   Therefore:
   \[
   f(g(x)) = (x - 1) + 1 = x
   \]

So, \( (f \circ g)(x) = x \).

### The correct answer is **D) x**.

Would you like more details or have any questions?

Here are 5 related questions to expand this concept:
1. What is the general process for composing two functions?
2. How would the solution change if \( g(x) \) were different, such as \( g(x) = \sqrt{x - 1} \)?
3. Can you find the inverse of the function \( f(x) = x^5 + 1 \)?
4. How do you verify if two functions are inverses of each other?
5. What is the domain of \( f \circ g \) in this problem?

**Tip:** Always double-check simplifications, especially when dealing with roots and powers, to avoid common mistakes.

Si f(x) = x^5 + 1 y g(x) = 5√(x - 1), entonces el valor de (f ∘ g)(x) es:

Learn how to solve the composition of functions (f ∘ g)(x) where f(x) = x^5 + 1 and g(x) = 5√(x - 1). This problem involves using algebraic techniques to simplify expressions involving exponents and roots. Suitable for Grades 10-12.

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