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To solve this problem, let's go through the composition of functions step-by-step. We're given:

1. \( g(x) = x - 1 \)
2. \( (f \circ g)(x) = f(g(x)) = 2x^2 - 4x + 3 \)

Our goal is to find \( f(x) \).

### Step 1: Substitute \( g(x) \) into \( f(g(x)) \)
Since \( g(x) = x - 1 \), we replace \( g(x) \) in \( f(g(x)) \):
\[
f(x - 1) = 2x^2 - 4x + 3
\]

### Step 2: Determine the function \( f(x) \)
To find \( f(x) \), let \( u = x - 1 \). Then, \( x = u + 1 \). Substitute \( x = u + 1 \) into the expression \( 2x^2 - 4x + 3 \):

1. Substitute \( x = u + 1 \) into \( x^2 \):
   \[
   x^2 = (u + 1)^2 = u^2 + 2u + 1
   \]

2. Substitute \( x = u + 1 \) into \( -4x \):
   \[
   -4x = -4(u + 1) = -4u - 4
   \]

3. Combine terms to find \( f(u) \):
   \[
   f(u) = 2(u^2 + 2u + 1) - 4u - 4 + 3
   \]
   \[
   = 2u^2 + 4u + 2 - 4u - 4 + 3
   \]
   \[
   = 2u^2 + 1
   \]

So, \( f(x) = 2x^2 + 1 \).

### Answer
The correct answer is:
**E. \( f(x) = 2x^2 + 1 \)**

Would you like further details or have any questions?

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### Related Questions

1. How do we solve for \( f(x) \) if \( (f \circ g)(x) \) has a different form?
2. What are the steps to verify if two functions are inverses of each other?
3. How would the solution change if \( g(x) \) was a more complex function?
4. How do we compute the composition of three functions?
5. What are real-world applications of function composition?

### Tip
In function composition, always substitute the inner function result first, then simplify.

Jika diketahui g(x) = x - 1 dan (f o g)(x) = 2x^2 - 4x + 3, fungsi f(x) adalah .... A. x - 2 B. x + 2 C. x^2 + 2 D. 2x^2 - 1 E. 2x^2 + 1

Solve for the function f(x) given the composition (f o g)(x) = 2x^2 - 4x + 3 and g(x) = x - 1. This problem involves function composition, algebraic expansion, and identifying quadratic functions. Detailed step-by-step solution included, suitable for students in Grades 10-12.

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