Answered

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Question 1 of 10, Step 3 of 3

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]

Step 3 of 3: Evaluate this function at \( x = -5 \). Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined".

[tex]\[
f(-5) =
\][/tex]

[tex]\[ \square \][/tex] Undefined

Sagot :

GinnyAnswer
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]
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