To solve for the missing values [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex], we need to evaluate the function [tex]\( g(x) = 4^{\frac{1}{2} x} \)[/tex] at specific values of [tex]\( x \)[/tex].
Step-by-Step Solution:
1. Finding [tex]\( A \)[/tex] when [tex]\( x = -2 \)[/tex]:
[tex]\[
g(-2) = 4^{\frac{1}{2} (-2)}
\][/tex]
[tex]\[
= 4^{-1}
\][/tex]
[tex]\[
= \frac{1}{4}
\][/tex]
2. Finding [tex]\( B \)[/tex] when [tex]\( x = 0 \)[/tex]:
[tex]\[
g(0) = 4^{\frac{1}{2} (0)}
\][/tex]
[tex]\[
= 4^0
\][/tex]
[tex]\[
= 1
\][/tex]
3. Finding [tex]\( C \)[/tex] when [tex]\( x = 2 \)[/tex]:
[tex]\[
g(2) = 4^{\frac{1}{2} (2)}
\][/tex]
[tex]\[
= 4^{1}
\][/tex]
[tex]\[
= 4
\][/tex]
So, after applying the function [tex]\( g(x) \)[/tex] for each required [tex]\( x \)[/tex], the missing values are:
[tex]\[
\begin{aligned}
A &= \frac{1}{4} \\
B &= 1 \\
C &= 4
\end{aligned}
\][/tex]
