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Consider the following piecewise-defined function.

[tex]\[
f(x)=\left\{\begin{array}{ll}
5x - 1 & \text{if } x \ \textless \ -3 \\
-3x - 1 & \text{if } x \geq -3
\end{array}\right.
\][/tex]

Evaluate this function at \( x = -1 \). Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined".

[tex]\[ f(-1) = \][/tex]

[tex]\[ \square \text{ Undefined} \][/tex]

Sagot :

GinnyAnswer
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].
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