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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

Learn how to evaluate the function f(x) = -3/(2x+1) at x = 1/2 with a detailed step-by-step solution. This problem involves function evaluation and rational functions. Suitable for students in Grades 9-12.

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