To simplify the function $f(x) = \frac{4x - 1}{2x + 3}$, follow these steps:

1. Identify common factors: First, check if there's a common factor in both the numerator and the denominator that can be factored out. In this case, the expressions $4x - 1$ and $2x + 3$ do not have a common factor.

2. Factorization (if possible): Check if either the numerator or denominator can be factored further. Here, both are already in their simplest linear forms.

3. Check for simplification: Since there are no common factors and both expressions are linear, the function is already in its simplest form.

So, the simplified form of the function is:

$f(x) = \frac{4x - 1}{2x + 3}$

This is as simplified as the function can be.

Would you like more details or have any questions? Here are five related questions that might interest you:

1. How do you determine when a rational function can be simplified?
2. What is the domain of the function $f(x) = \frac{4x - 1}{2x + 3}$?
3. How do you find the vertical asymptotes of a rational function?
4. What are the intercepts of the function $f(x) = \frac{4x - 1}{2x + 3}$?
5. How can you find the horizontal asymptote of a rational function?

Tip: Always check for common factors between the numerator and the denominator before concluding that a rational function is fully simplified.