Answered

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Consider the following piecewise-defined function:

[tex]\[ f(x) = \begin{cases}
5x - 1 & \text{if } x \ \textless \ -3 \\
-3x - 1 & \text{if } x \geq -3
\end{cases} \][/tex]

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

[tex]\[ f(-3) = \][/tex]
[tex]\[ \square \][/tex] Undefined

Sagot :

GinnyAnswer
To evaluate the piecewise-defined function \( f(x) \) at \( x = -3 \), we need to determine which piece of the function to use.

Given the function:
[tex]\[ f(x) = \left\{\begin{array}{ll} 5x - 1 & \text{if} \, x < -3 \\ -3x - 1 & \text{if} \, x \geq -3 \end{array}\right. \][/tex]

We see that \( x = -3 \) falls into the condition \( x \geq -3 \). Therefore, we will use the second piece of the function, which is \( -3x - 1 \).

Now, substituting \( x = -3 \) into this equation:
[tex]\[ f(-3) = -3(-3) - 1 \][/tex]

First, compute the multiplication part:
[tex]\[ -3 \times -3 = 9 \][/tex]

Next, subtract 1 from the result:
[tex]\[ 9 - 1 = 8 \][/tex]

Thus, the value of \( f(-3) \) is:
[tex]\[ f(-3) = 8 \][/tex]
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