https://file.aiquickdraw.com/mathbot/file/17267821797796lake87l.jpg

The problem asks you to find \( g(x) \), given that:

\[
f \circ g(x) = 2x^2 - 4x + 3 \quad \text{and} \quad f(x) = 2x - 1
\]

### Step-by-step solution:

1. The composition \( f \circ g(x) \) means that:
   \[
   f(g(x)) = 2x^2 - 4x + 3
   \]
2. Since \( f(x) = 2x - 1 \), we replace \( f(g(x)) \) with \( 2g(x) - 1 \):
   \[
   2g(x) - 1 = 2x^2 - 4x + 3
   \]
3. Now, solve for \( g(x) \):
   \[
   2g(x) = 2x^2 - 4x + 3 + 1
   \]
   \[
   2g(x) = 2x^2 - 4x + 4
   \]
4. Divide both sides by 2:
   \[
   g(x) = x^2 - 2x + 2
   \]

Thus, \( g(x) = x^2 - 2x + 2 \).

Would you like further details or explanations? Here are some additional questions to explore this topic:

1. What is the general process for solving a composite function problem?
2. How do you verify the solution of a composite function problem like this one?
3. Can you explain the difference between \( f(g(x)) \) and \( g(f(x)) \)?
4. What would the process look like if the function \( f(x) \) were more complex?
5. How can solving composite functions help in real-world applications?

**Tip**: When working with composite functions, make sure you substitute the inner function correctly into the outer one to avoid errors.

Diketahui f∘g(x) = 2x^2 − 4x + 3 dan f(x) = 2x − 1. Tentukanlah g(x)!

Learn how to find g(x) in a function composition problem where f∘g(x) = 2x^2 − 4x + 3 and f(x) = 2x − 1. This solution involves key algebraic concepts such as function composition and solving quadratic equations. Suitable for students in Grades 9-11.

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