Answer :
To evaluate the piecewise-defined function \( f(x) \) at \( x = -1 \), follow these steps:
1. Identify the correct piece for \( x = -1 \):
The function \( f(x) \) is defined as:
[tex]\[ f(x) = \left\{\begin{array}{ll} 5x - 1 & \text{if } x < -3 \\ -3x - 1 & \text{if } x \geq -3 \end{array}\right. \][/tex]
Since \( -1 \geq -3 \), we use the second piece of the function: \( f(x) = -3x - 1 \).
2. Substitute \( x = -1 \) into the selected piece:
Substitute \( x = -1 \) into \( f(x) = -3x - 1 \):
[tex]\[ f(-1) = -3(-1) - 1 \][/tex]
3. Simplify the expression:
[tex]\[ f(-1) = 3 - 1 = 2 \][/tex]
Therefore, the value of the function at [tex]\( x = -1 \)[/tex] is [tex]\( \boxed{2} \)[/tex].
1. Identify the correct piece for \( x = -1 \):
The function \( f(x) \) is defined as:
[tex]\[ f(x) = \left\{\begin{array}{ll} 5x - 1 & \text{if } x < -3 \\ -3x - 1 & \text{if } x \geq -3 \end{array}\right. \][/tex]
Since \( -1 \geq -3 \), we use the second piece of the function: \( f(x) = -3x - 1 \).
2. Substitute \( x = -1 \) into the selected piece:
Substitute \( x = -1 \) into \( f(x) = -3x - 1 \):
[tex]\[ f(-1) = -3(-1) - 1 \][/tex]
3. Simplify the expression:
[tex]\[ f(-1) = 3 - 1 = 2 \][/tex]
Therefore, the value of the function at [tex]\( x = -1 \)[/tex] is [tex]\( \boxed{2} \)[/tex].
