To evaluate the piecewise-defined function at \( x = -5 \), we need to determine which part of the function to use based on the value of \( x \).
The function \( f(x) \) is defined as follows:
[tex]\[
f(x) =
\begin{cases}
5x - 1 & \text{if } x < -3 \\
-3x - 1 & \text{if } x \geq -3
\end{cases}
\][/tex]
Given \( x = -5 \):
1. We need to check the condition \( x < -3 \).
- Since \( -5 < -3 \) is true, we use the first part of the function, which is \( 5x - 1 \).
Now, let's substitute \( x = -5 \) into the first part of the function:
[tex]\[
f(x) = 5(-5) - 1
\][/tex]
Next, we perform the calculation:
[tex]\[
f(-5) = 5(-5) - 1 = -25 - 1 = -26
\][/tex]
Thus, the value of the function at \( x = -5 \) is:
[tex]\[
f(-5) = -26
\][/tex]
The answer is:
[tex]\[
\boxed{-26}
\][/tex]
