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.