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In the problem, you are given the following information:

1. \( f(x) = 2x - 1 \)
2. \( g(x) = \frac{5x}{x + 1} \)
3. \( (g \circ h)(x) = x - 2 \)

You are asked to find \( (h \circ f)(x) \).

### Step-by-Step Solution:

1. **Understanding the composite function** \( (g \circ h)(x) \):
   \[
   (g \circ h)(x) = g(h(x)) = x - 2
   \]
   This means that \( g(h(x)) = \frac{5h(x)}{h(x) + 1} = x - 2 \).

2. **Solve for \( h(x) \)**:
   Set up the equation using the expression for \( g(h(x)) \):
   \[
   \frac{5h(x)}{h(x) + 1} = x - 2
   \]
   Now, cross-multiply to solve for \( h(x) \):
   \[
   5h(x) = (x - 2)(h(x) + 1)
   \]
   Expand the right-hand side:
   \[
   5h(x) = (x - 2)h(x) + (x - 2)
   \]
   Bring all terms involving \( h(x) \) to one side:
   \[
   5h(x) - (x - 2)h(x) = x - 2
   \]
   Factor out \( h(x) \):
   \[
   h(x)(5 - (x - 2)) = x - 2
   \]
   Simplify the expression:
   \[
   h(x)(7 - x) = x - 2
   \]
   Solve for \( h(x) \):
   \[
   h(x) = \frac{x - 2}{7 - x}
   \]

3. **Find \( (h \circ f)(x) \)**:
   Now, substitute \( f(x) = 2x - 1 \) into \( h(x) \):
   \[
   (h \circ f)(x) = h(f(x)) = h(2x - 1)
   \]
   Substitute \( 2x - 1 \) into the expression for \( h(x) \):
   \[
   h(2x - 1) = \frac{(2x - 1) - 2}{7 - (2x - 1)}
   \]
   Simplify the numerator and denominator:
   \[
   h(2x - 1) = \frac{2x - 3}{8 - 2x}
   \]

Thus, the expression for \( (h \circ f)(x) \) is:
\[
\frac{2x - 3}{-2x + 8}
\]

### Answer:
The correct choice is **D**.

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Would you like more details or have any further questions? Here are five related questions to expand on this:

1. What is the definition of a composite function, and how does it work?
2. How would the solution change if \( g(x) \) were different?
3. Can you explain the process of solving for \( h(x) \) in more detail?
4. How can we verify that our solution for \( h(x) \) is correct?
5. What are some common mistakes when working with composite functions?

**Tip**: When solving for a function within a composite, always carefully handle the algebraic manipulation to avoid errors.

Diketahui f(x) = 2x - 1 dan g(x) = 5x/(x + 1). Jika b adalah fungsi sehingga (g o h)(x) = x - 2, maka (h o f)(x) = ...

In this problem, learn how to find the composite function (h o f)(x) by solving a system of composite equations using f(x) = 2x - 1 and g(x) = 5x/(x + 1). Step-by-step explanation provided for solving this algebraic composite function problem suitable for high school students.

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