Answer:
Option B: 1
Step-by-step explanation:
Given the piecewise-defined function rules:
[tex]\displaystyle\mathsf{\left g(x)=\Bigg\{{{\sqrt[3]{x+5},\quad\ x\leq -4} \atop {-x^2+11,\quad\ x\:>-4}} \right. }[/tex]
The piecewise-defined function defines the rules over specific intervals of its domain.
In order to find the value of g( –4), we must first determine which piecewise-defined function applies to an input value of x = –4. This input value does not fall under the second piecewise-defined function since the input , x > –4 Thus, x = -4 is not included as part of the solution.
The piecewise-defined function that applies to g( –4) is [tex]\displaystyle\mathsf{g(x)=\:\sqrt[3]{x+5}}[/tex] because of the rule, "x ≤ –4."
All we need to do at this point is to substitute the input value into the following piecewise-defined function:
[tex]\displaystyle\mathsf{g(x)=\:\sqrt[3]{x+5}}[/tex]
[tex]\displaystyle\mathsf{g(-4)=\:\sqrt[3]{-4+5}}[/tex]
[tex]\displaystyle\mathsf{g(-4)=\:\sqrt[3]{1}}[/tex]
[tex]\displaystyle\mathsf{g(-4)=\:1}[/tex]
Therefore, the value of g( –4) = 1, which makes Option B the correct answer.
