To find the value of [tex]\( g(-4) \)[/tex], we need to determine which part of the piecewise function [tex]\( g(x) \)[/tex] we should use. The function is defined 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 we are asked to find [tex]\( g(-4) \)[/tex] and [tex]\(-4 \leq -4\)[/tex], we use the first part of the piecewise function:
[tex]\[
g(x) = \sqrt[3]{x + 5}
\][/tex]
Now, substitute [tex]\( x = -4 \)[/tex] into this equation:
[tex]\[
g(-4) = \sqrt[3]{-4 + 5}
\][/tex]
Simplify the expression inside the cube root:
[tex]\[
-4 + 5 = 1
\][/tex]
So, we have:
[tex]\[
g(-4) = \sqrt[3]{1}
\][/tex]
Since the cube root of 1 is 1:
[tex]\[
g(-4) = 1
\][/tex]
Therefore, the correct answer is:
A. 1
