To determine the value of [tex]\( f(g(0)) \)[/tex], we need to follow these steps:
1. Find [tex]\( g(0) \)[/tex]:
We will look up the value of the function [tex]\( g \)[/tex] when [tex]\( x = 0 \)[/tex] from the given table. According to the table:
[tex]\[
g(0) = -1
\][/tex]
2. Find [tex]\( f(g(0)) \)[/tex]:
Now that we know [tex]\( g(0) = -1 \)[/tex], the next step is to find the value of the function [tex]\( f \)[/tex] when [tex]\( x = -1 \)[/tex]. According to the table:
[tex]\[
f(-1) = 1
\][/tex]
Therefore, [tex]\( f(g(0)) = f(-1) = 1 \)[/tex].
So, the value of [tex]\( f(g(0)) \)[/tex] is [tex]\( 1 \)[/tex].
