To determine the value of the function $f(x) = -\frac{3}{2x+1}$ when $x = \frac{1}{2}$, we need to substitute $x = \frac{1}{2}$ into the function and simplify.

Given: $f(x) = -\frac{3}{2x+1}$ Substitute $x = \frac{1}{2}$: $f\left( \frac{1}{2} \right) = -\frac{3}{2\left( \frac{1}{2} \right) + 1}$

Now, simplify the expression in the denominator: $2\left( \frac{1}{2} \right) + 1 = 1 + 1 = 2$

Thus, the function becomes: $f\left( \frac{1}{2} \right) = -\frac{3}{2}$

Therefore, the value of the function when $x = \frac{1}{2}$ is: $f\left( \frac{1}{2} \right) = -\frac{3}{2}$

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

Here are some related questions to consider:

1. What is the domain of the function $f(x) = -\frac{3}{2x+1}$?
2. How do you find the vertical asymptote of the function $f(x) = -\frac{3}{2x+1}$?
3. What is the behavior of the function $f(x) = -\frac{3}{2x+1}$ as $x$ approaches the vertical asymptote?
4. How can you determine