To determine the value of [tex]\( g(-4) \)[/tex], we need to evaluate the function [tex]\( g(x) \)[/tex] at [tex]\( x = -4 \)[/tex]. The function [tex]\( g(x) \)[/tex] is defined piecewise as follows:
[tex]\[
g(x) =
\begin{cases}
\sqrt[3]{x+5}, & \text{if } x \leq -4 \\
-x^2 + 11, & \text{if } x > -4
\end{cases}
\][/tex]
Since [tex]\(-4 \leq -4\)[/tex], we use the first part of the piecewise function:
[tex]\[
g(x) = \sqrt[3]{x + 5}
\][/tex]
Substitute [tex]\( x = -4 \)[/tex] into the function:
[tex]\[
g(-4) = \sqrt[3]{-4 + 5}
\][/tex]
Simplify the expression inside the cube root:
[tex]\[
g(-4) = \sqrt[3]{1}
\][/tex]
The cube root of 1 is:
[tex]\[
g(-4) = 1
\][/tex]
Thus, the value of [tex]\( g(-4) \)[/tex] is 1. The correct answer is:
C. 1
