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The problem is asking for the value of \( f(-5) \) in the given piecewise function:

\[
f(x) = 
\begin{cases} 
-3x + 1 & \text{when } x > 1 \\
-2x & \text{when } x = 1 \\
2x - 1 & \text{when } x < 1
\end{cases}
\]

Since \( x = -5 \), and \(-5 < 1\), we use the third piece of the function:

\[
f(x) = 2x - 1 \quad \text{for} \quad x < 1.
\]

Substitute \( x = -5 \):

\[
f(-5) = 2(-5) - 1 = -10 - 1 = -11.
\]

Thus, \( f(-5) = -11 \).

The correct answer is \(-11\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the value of \( f(2) \) in this piecewise function?
2. How do you determine which piece of the function to use for \( f(x) \)?
3. What is the value of \( f(1) \)?
4. How would you graph this piecewise function?
5. What would happen if \( x = 0 \) in the piecewise function?

**Tip**: Always check the domain conditions before evaluating a piecewise function.

What is the value of f(-5) in the piecewise function f(x) = { -3x + 1, when x > 1; -2x, when x = 1; 2x - 1, when x < 1 }?

Learn how to evaluate f(-5) in the given piecewise function f(x). This problem explains how to choose the correct piece of the function based on the input value and provides a step-by-step solution. Suitable for Grades 9-12.

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