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I have loaded the image. It contains the mathematical problem related to a function \( g(x) = x^2 - 2x + 5 \), and it asks to find \( g(2x) \). Let me calculate that for you.

We are given the function \( g(x) = x^2 - 2x + 5 \), and we need to find \( g(2x) \). This means we substitute \( 2x \) for every \( x \) in the original function expression:

\[
g(2x) = (2x)^2 - 2(2x) + 5
\]

Now simplify the expression:

\[
g(2x) = 4x^2 - 4x + 5
\]

Thus, the expression for \( g(2x) \) is \( 4x^2 - 4x + 5 \).

Would you like more details or clarification? 

Here are some related questions:
1. What does the function \( g(x) \) represent graphically?
2. How would you evaluate this function at a specific value of \( x \)?
3. How does this type of function relate to quadratic functions?
4. What is the vertex form of this quadratic function?
5. How can you solve for \( x \) in the equation \( g(x) = 0 \)?

Tip: Quadratic functions always have a parabolic shape when graphed, and their vertex can be found using the formula \( x = -\frac{b}{2a} \) where \( a \) and \( b \) are the coefficients of \( x^2 \) and \( x \), respectively.

Given the function defined by g(x) = x^2 - 2x + 5, find g(2x). Express the answer in simplest form.

Learn how to calculate g(2x) when given the function g(x) = x^2 - 2x + 5. This problem covers key algebraic concepts, including substitution in functions and simplifying quadratic expressions. Suitable for students in Grades 9-10.

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