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We are given the functions:

1. \( f(x) = \frac{1 - x}{x} \), with \( x \neq 0 \).
2. \( g(x) = x + 2 \).

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

### Step 1: Find \( f(x) \)

We have:
\[
f(x) = \frac{1 - x}{x} = \frac{1}{x} - 1.
\]

### Step 2: Substitute \( f(x) \) into \( g(x) \)

Since \( (g \circ f)(x) = g(f(x)) \), we substitute \( f(x) = \frac{1 - x}{x} \) into \( g(x) = x + 2 \):

\[
g(f(x)) = g\left(\frac{1 - x}{x}\right) = \frac{1 - x}{x} + 2.
\]

### Step 3: Simplify \( g(f(x)) \)

To add \( \frac{1 - x}{x} \) and \( 2 \), we write \( 2 \) as \( \frac{2x}{x} \):

\[
g(f(x)) = \frac{1 - x}{x} + \frac{2x}{x} = \frac{1 - x + 2x}{x} = \frac{1 + x}{x}.
\]

### Answer

Thus, \( (g \circ f)(x) = \frac{1 + x}{x} \).

Looking at the answer choices, the correct answer is:
\[
\text{D. } \frac{1}{x} + 1 = \frac{1 + x}{x}.
\]

Would you like more details on any step, or have any questions?

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Here are some related questions to explore further:

1. How do we find the domain of a composite function?
2. What are the properties of composite functions?
3. Can we break down composite functions involving rational expressions further?
4. How would the answer change if \( g(x) \) were different?
5. How do we find the inverse of a composite function?

**Tip:** When working with compositions, always carefully substitute and simplify, especially if fractions are involved.

Diketahui f(x) = (1 - x) / x, x ≠ 0 dan g(x) = x + 2. Hasil dari (g ∘ f)(x) adalah ...

Learn how to find the composition of functions with rational expressions. Given f(x) = (1 - x) / x and g(x) = x + 2, this problem guides you through finding (g ∘ f)(x) with step-by-step solutions. Suitable for high school algebra students.

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