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Sagot :
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]
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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