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The question is asking to express \( y = 2x + 3 \) in terms of \( f(x) \). Let's go through the steps to rewrite this equation:

1. Start with the given equation:
   \[
   y = 2x + 3
   \]

2. To express this in terms of \( x \), solve for \( x \):
   \[
   y - 3 = 2x
   \]

3. Divide by 2 to isolate \( x \):
   \[
   \frac{y - 3}{2} = x
   \]

4. Rewrite \( x \) as \( f(x) \):
   \[
   f(x) = \frac{y - 3}{2}
   \]

Now let's compare this with the options given:

- a. \( f(x) = 2x = y - 3 \)
- b. \( f(x) = 2x = y - 3/2 \)
- c. \( f(x) = 2x = y - 2 \)
- d. \( f(x) = x = 2 - y \)
- e. \( f(x) = x = 2/3 - y \)

None of the options seem to directly match the form we derived, \( f(x) = \frac{y - 3}{2} \). However, option **b** is the closest in structure, but it should be corrected as \( f(x) = \frac{y - 3}{2} \).

To match exactly, the correct expression would be \( f(x) = \frac{y-3}{2} \). It seems the question might be testing understanding of isolating \( x \) in terms of \( y \), and none of the given options directly match the derived form.

Would you like more details or have any questions about this problem?

Here are 5 related questions for further practice:

1. How do you solve for \( x \) in linear equations of the form \( y = mx + b \)?
2. What is the inverse function of \( y = 2x + 3 \)?
3. How do you check if two functions are inverses of each other?
4. Can you express \( y = 3x + 2 \) in terms of \( f(x) \)?
5. How would you graph the function \( y = 2x + 3 \) and its inverse?

**Tip:** Always isolate the variable you need to express in terms of another variable, and rearrange the equation systematically to avoid errors.

Learn how to express the function y = 2x + 3 in terms of f(x). This algebra problem involves solving for x in linear equations and applying function transformations. Suitable for students in Grades 8-10.

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